Solving Logarithmic Equations… How? (NancyPi)

Published on October 7, 2018 by

MIT grad shows how to solve log equations, using LOG PROPERTIES to simplify and solve. To skip ahead: 1) For solving BASIC LOG EQUATIONS, skip to 0:22. 2) For ONE LOG ON EACH SIDE (EQUALITY property), skip to 2:36. 3) For TWO LOGS ADDED together and equaling a number (PRODUCT property), skip to 5:25. 4) For MANY LOGS, SUBTRACTED and ADDED, and using the QUOTIENT property, POWER property, and the other properties of logarithms (log rules), skip to 9:53. This video focuses on solving logarithms in equations and explains how to check the solution for an extraneous solution. Nancy formerly of MathBFF explains the steps.

For my video on logarithm basics like how to EVALUATE LOGS, including natural logs (ln x), jump to:

Follow Nancy on Instagram:

SOLVING LOGARITHMIC EQUATIONS for x: Every logarithm is connected to an exponential form. The best way to figure out a log function is to REARRANGE THE LOG INTO EXPONENTIAL FORM and then solve for x. I show a quick recap of how to rewrite a log into exponential form, but for a longer explanation of rearranging into exponential form to evaluate a log, jump to my video "Logarithms... How?" ( for help with converting log to exponential form. In this video, I show you more complicated log equations with more than one log, where you'll need the LOG PROPERTIES (logarithm rules) to simplify and be able to condense down to one logarithm on a side so that you can solve.

Solving logarithmic equations with LOGS ON BOTH SIDES: If you have one log on each side of the equation, with the same base, you can use the EQUALITY PROPERTY log formula.

If you have more than one log on a side of the equation (with the same base), you can use the PRODUCT PROPERTY (if the logs are added) or the QUOTIENT PROPERTY (if the logs are subtracted) to combine the logs into one log. If you have a number multiplied in front of a log, as a coefficient, you can use the POWER PROPERTY logarithm formula to bring the coefficient up as a power inside the log argument. Once you simplify the log equation using the product, quotient, and/or power properties, you can either 1) solve by using the equality property if you just have one log on each side (with same base), or 2) solve by rewriting into exponential form if you have a log on one side and a number on the other side. IMPORTANT - CHECK SOLUTIONS: When solving logarithmic functions, you have to CHECK your solutions for log equations. Any numbers you get as solutions you have to plug back into the original equation to check. If a solution does not work or gives an undefined value (for example: log of a negative number), then it is an "extraneous solution" and must be thrown out!

For more logarithm examples and help with solving logarithmic and exponential equations, logarithmic form problems, exponential function and exponential equation math, solving logarithmic expressions, solving log equations without a calculator, log x equations, exponential and logarithmic functions, exponent math, log solver and log equation solver math, log equations with the same base, and log equations with different bases, as well as more of my math videos for algebra, algebra 2, precalculus, and college algebra, check out:

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Advertise here. Telegram, Signal - Call/message +1-868-308-4028.


  • Muhammad 4 years ago

    Hey Nanci

  • reznoire 4 years ago

    Yay 1080p

  • haji alhaeri 4 years ago

    love the channel best of luck

  • amty 4 years ago

    i wish i could solve you

    • BlocknBoom! 4 years ago

      amty haaaa

    • Utente 4 years ago

      BlocknBoom! ๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚

    • Kiko Garcia 4 years ago

      lol same shes beautiful

  • hamisu Physics 4 years ago

    thanks Nancy love this channel always comes at right time

  • Sebastian 4 years ago

    just clicked to say hi ๐Ÿ™‚

  • Greg Edwards 4 years ago

    Thank you Nancy. Very helpful. l think I finally get it now. Keep up the good work.

  • Thor Odinson 4 years ago

    Thank you Nancy, Very Pi!

    • Juggernaut 4 years ago

      Oh yeah yeah

  • Carlton Davis 4 years ago

    You’re funny, Nancy.

  • Luqman Arif 4 years ago

    Can you teach us laplace transform please

  • Brock Sullivan 4 years ago

    Hey I’m in calc 3 and slightly dying. Could you do any videos on calc 3.

  • OrphanPaper 4 years ago

    Thanks Nancy my math is like my art ,divergent from reality ,

  • Odra Rdz 4 years ago

    queen of math

  • ragava r 4 years ago

    Ur video are interesting it is boosting up me to do math….thank you soooo much nancy ma’am…๐Ÿค—๐Ÿค—๐Ÿค—๐Ÿค—

    • shawn Jacob 4 years ago

      ragava r u are creepy

    • The BlackMace 2 years ago

      @shawn Jacob Is that a question or what?

    • shawn Jacob 2 years ago

      Nope if you look closely with you useless brain his user name it is ragava r so I stated u are creepy.

    • The BlackMace 2 years ago

      @shawn Jacob Oh! lol My bad.

  • charmant beaugarcon 4 years ago

    Big respect; big love; big thanks

  • TI Ted 4 years ago

    very clear and educational – maths does not get any better than this

  • Uriah Siner 4 years ago

    Would log base 2 of -2 equal 1i?

    • Penguin Bros 4 years ago

      does 2^i = -2?

      It doesn’t since i is imaginary and if you plug it into a calculator, any log won’t have a negative base.

    • Joris Janssens 4 years ago

      From watching lots of blackpenredpen video’s, I would think it’s (ln(2)+ iฯ€)/ln(2). Note that e^(iฯ€)=-1 (Euler). So we can rewrite log2(-2) as log2(2e^(iฯ€)). Then switch to natural logaritm: ln(2e^(iฯ€))/ln(2) Split up the top logarithm: (ln(2)+ln(e^(iฯ€))/ln(2) And finally the logarithm en e cancel out so we get: (ln(2) + iฯ€)/ln(2)

  • Zuhair S 4 years ago

    Ty on same topic next video maybe solving logs with ln and e if you like.

  • Mark 4 years ago

    hey where nancy merch pls nancy

  • yupitskari 4 years ago

    At some point I just started watching your videos even though I don’t need it

    • Eklavya Goyal 3 years ago

      Lmao same

    • Leo Volont 3 years ago

      It is extra fun if you get a few White Boards and Dry Erase Markers so that you can work along. What I did was I got 11by14 inch Glass Picture Frames and inserted White Paper under the glass, and I use Fine Tip Expo Dry Erase Markers. I whip out the work before she does it, so that I basically know what she is going to say, but then if she has some special trick or some proviso, then it catches my attention because of the “why didn’t I think of that” factor

  • Andrew 4 years ago

    you make every section of precalc-calculus a lot easier! I was wondering if you could explain l’hopital’s rule in an easier form?

  • Iidiotic 4 years ago

    just stumbled upon your channel and I like how you explain. Therefore I would kindly ast you to please explain the Gaus elimination. I am really having a hard time with it because I keep going back and forth and I can’t create the stupid triangle :DD thx

  • Cody Brown 4 years ago

    Oh, my god.

  • Moe Haroun 4 years ago

    love yaaaaaaaaaaaaaaaaaaaaaaaaaaaa

  • Shaan Tiwari 4 years ago

    Thank you very much, ma’am

  • ccsvenezuela2006 4 years ago

    I never closed Khan Academy so fast ๐Ÿ™‚

    • Veritas et Aequitas 3 years ago

      Right? Sal trying to explain that multiplying logs was a nightmare with no good explanation.
      Also, she FF through the writing where Sal.. repeats himself.. repeats.. repeats… Himself… Himself… Himmm.. seeelf… Constantly because he doesn’t dare leave a moment not filled by his own voice.

    • Creative Razor 3 years ago


    • rgftown1 3 years ago


    • Na Zombie 2 years ago

      She the new Sam Khan!! Just even better

    • David Ricardo 2 years ago

      Sal Khan is not this HOT

  • Smauel 4 years ago

    Could you talk about how to solve improper integration please? Thank you Nancy. Love you

  • Kevin Nichols 4 years ago


  • Kevin Nichols 4 years ago

    Can you explain using derivate tests to find extremas?

  • Nandan Shah 4 years ago


  • Colleen Dennehy 4 years ago

    Can you do a video on the derivative of inverse trig functions please?!!!!!

  • Ishant Gadhave 4 years ago

    If the base of any logarithmic term is 1/x or x^2 or | x+2 | … For example if the que says log (x^2- 5/2x +1) to the base 3x/(x^2+1) is greater than or equal to zero.. Find the possible values of x??? How to solve these

  • sammy124 4 years ago

    You gotta know you have LITERALLY SAVED MY LIFE through these videos. bless your heckin soul !!!

    • Eflo 3 years ago


    • Josh Cuneo 3 years ago

      Eflo maybe they meant literally

  • daniel lynes 4 years ago

    Thank you so much

  • El lord Ali 4 years ago

    Keep going itโ€™s nice to learn more from a gorgeous angel

  • Mwila Arthur 4 years ago

    Hey Nancy can you please please please make a binomial theorem video we’d really appreciate it

  • Arthur Middenway 4 years ago

    what do we do with the variable “wtf” again?

    • Decaf-Math ASMR 4 years ago

      lol, solve for “wtf”?

  • SD Hadoken 4 years ago

    Senpai ๐Ÿ™

  • Clark Huppert 4 years ago

    Wow you actually make this simple to understand. I have gone over and struggled through logarithms before but I never retain it. This is a great reference video, thank you.

  • Elton Lucien 4 years ago

    Thanks a bunch, I have a final exam next week, and my prof kinda breezed through the exp/log functions chapters. Perfect timing!

  • Carlosk12 4 years ago

    What if the logs don’t have the same base

  • Rafold Starking 4 years ago

    NancyPi. Your explanation is so efficient and elegant. Iโ€™ve got to follow you! On a side note, it was easier for me to follow your reasoning having reviewed the properties of exponents. But I wonder if it is going to make as much sense for first timers.

  • sujita singh 4 years ago

    Just one question…… 9:38 the working done on the right side is somehow appearing something of a contradiction to what you just said. Won’t that -2 & -4 multiply to give +8 which could make the values true for the given problem???

    • Per-Axel Skogsberg 4 years ago

      It would be 8 after simplification, but you always need to verify that it works in the provided original form. For example (x(x-1))/(x-1)=x can be simplified to x=x which holds true for all real values of x. But we still can’t let x be 1 because that would make division by 0 if put in the first form of the equation.

    • Joshua Tovar 4 years ago

      One simple explanation: Just remember that log(-x), where is any real number, is non-existent. I think it gets mentioned at 9:12 thanks

    • Angel Eduardo 4 years ago

      You can’t raise a number by a power and get a negative result

  • Prof L Axis 4 years ago

    Maths Queen of Sciences, NancyPi a new Queen of Maths. What a discovery!

  • Alex Chavez 4 years ago

    Thank you NancyPi for helping me understand logs. I was very confused from a college pre-calculus lecture. Now I am confident in this subject and have no doubt I will do well in quiz day.

  • Angela Seleke 4 years ago

    Thank you Nancy,you make maths fun for me <3

  • James Corbin 4 years ago

    Relearning math after having been out of school for a while. Subscribed. Thanks

  • Senzekile Sibiya 4 years ago

    Daaaamn these thing is sooo easy come im only seeing your videos now…u saved my life ..i hated logs cause i didnt understand them..thank u sooo much

    • Joel Acosta 4 years ago

      Senzekile Sibiya sammeee

    • Jiminlesmolbean _ 4 years ago

      Same ๐Ÿ˜”

    • SmileyBoySa Gaming 3 years ago

      logs are ez dafuq do u mean

    • InfiniteLoop 3 years ago

      @SmileyBoySa Gaming Agreed. For me trig is harder because of all the fucking memorising I have to do๐Ÿ˜ญ

  • Iron Men 4 years ago

    Fantastic ๐Ÿ‘Œ๐Ÿป

  • qilah 4 years ago


  • Rebal Hadi 4 years ago

    call me

  • Wade McKenzie 4 years ago

    Thank You NANCY!!!!!!

  • Amr Abdalla 4 years ago

    Jesus christ, do u guys realize that shes writing in mirror handwriting, shes so good wtf

    • Nick Benson 4 years ago

      She flips the video my g

    • chris Bruner 4 years ago

      And she’s doing it left handed!

    • The BlackMace 2 years ago

      She mirrors the video. ๐Ÿคฆ

  • John Kenny 4 years ago

    The rules are collected so clearly

  • Aiana Primus 4 years ago

    where did the +7 on both sides come from in question 1

  • Andriene Francis 4 years ago

    funny how i’m in math class and couldn’t seem to grasp this until seeing your video. just in time before my mid semester test ๐Ÿ™‚

  • Michael Spurlock 4 years ago

    Where can I find more practice problems for logs?

  • Jake 4 years ago

    @nancypi do you have to write backwards to make our view look correct? mind freak…

  • Eli Groisman 4 years ago

    Explained beautifully, in a simple way.

  • Hey It's me 4 years ago

    Wooowww thank you sooo much!! You taught it so clearly I was so confused before !!

  • Maddie T 4 years ago

    I love that you’re beautiful and intelligent, keep up the good work & thank you for your help
    -distressed students united

  • OTG Label 4 years ago

    she never warned me of how beautiful she is :p

  • OTG Label 4 years ago

    Such a wonderful video, Twas helpful. Thank you!

  • Jay Khan 4 years ago

    fantastic vid mate

  • Saleh Jamal 4 years ago

    what happened to your last account you had more than 400k subscribers a.k.a mathbff

  • Savii Magnificent 4 years ago

    Thank you a lot this is truly amazing Nancy ….keep up the good job

  • Ak Thomas 4 years ago

    thank you so much

  • Chloe Yen 4 years ago

    Oh my god, she was writing normally! She used a mirror mode to make the video comprehensible.

    • Eduardo Galdino 3 years ago

      Yesmirror thats physics at work my left your righ,simmetric and real…

    • HypnoticChance 3 years ago

      @Eduardo Galdino symmetrical* lol

    • Kai Stahly 3 years ago

      thanks, I was wondering that the hole vid

    • Harry Ross 3 years ago

      @Vibe Goddess of Math for the common man

    • Cara Diann 2 years ago

      It sure is handy humans are (mostly) symmetrical!

  • Hillary Edwards 4 years ago

    You helped me pass my class last quarter. You are a great teacher. I learn a lot from you. Thank you!!

  • Sebastian Ochoa 4 years ago

    Gorgeous and smart ๐Ÿ™‚

  • Charity Pitts 4 years ago

    Thank you Nancy! Iโ€™m crying right now, Iโ€™m so happy. Iโ€™m scared to watch any other Videos because they may confuse me!

  • bewketu negash 4 years ago

    thank u very much [NancyPi]

  • Nicholas Sway 4 years ago

    @0:29 log-ithm ๐Ÿ˜‚๐Ÿ˜‚

  • David Posey 4 years ago

    Thank you so much! If you’re ever in Seattle, I owe ya a coffee ๐Ÿ™‚

  • NuNu Ding-Lam 4 years ago

    Is possible two difference log based within the function? if so, how to unify them into one

  • Nizam Nafeel 4 years ago

    I like you Nancy.i love you

  • Ramneek K 4 years ago

    Saved my life!!

  • whosMandoo 4 years ago

    Youโ€™re literally a godsend Nancy!!! Thank you so much ๐Ÿคž๐Ÿฝ๐Ÿ’• time to pass this math 41 final

  • Xรคp 8 4 years ago

    Thank you NANCY!!!!!!

  • chukchee 4 years ago

    The log of a negative number is imaginary.

  • chukchee 4 years ago

    Whats the point of knowing how to do this when computers can do this is nanoseconds?

  • T Stepp 4 years ago

    She is so beautiful, love a smart girl very hot. Body looks good too. Lol

  • Mosio Masoud 4 years ago

    Great ๐Ÿ‘๐Ÿป I can’t say I like math but it’s a fundamental language and u teach it really good! +1subbed!

  • ee-sai-EE Elizondo 4 years ago

    3:18 is me in my school choir everyday

    • Lewis Ong 4 years ago


  • Laura Thomas 4 years ago

    My students and I love your clear, neatly written, very well planned lessons.

    • aman dad 3 years ago

      why don’t u teach the class lmao tf i pay taxes for

    • Alfa 3 years ago

      @aman dad ๐Ÿ˜‚

  • RokWisdawn 4 years ago

    Do you play PC games, too, by any chance? ‘Cause if you do, then I’ll just embarrass myself miserably on the internets and assert that you’re unequivocally my soulmate and we should totally get married and have little nerdlings running around, constantly talking about how awesome maths and sciency things are. I’m a mature university student err … revising for an exam. It’s all true!

    No, wait! What I mean is … do NOT teach guys! It doesn’t work! Well, maybe it does … a little, but it mostly doesn’t. They’ll never 100% focus on algebra.

    Anyway, back to Khan Academy now before I say anything, at all, stupid.


    • Zeeshan Rafiq 4 years ago

      you wet don

    • picophd 4 years ago

      @Zeeshan Rafiq What’s that in English?

  • Hh Mm 4 years ago

    The best teacher. Thanx

  • Epic entertainment 4 years ago

    Nancy pi thanks
    Can you help me out with differential equations

  • Michael Vasquez 4 years ago

    I wish you were my teacher your are so god dam beautiful I will never fail my my math class because i wouldn’t be losing focus

  • Jan Broberg 4 years ago

    Very nice! I betcha video cam is recording in mirror mode – so you Nancy are writing with right hand ๐Ÿ˜œ. Anyhow – great!

  • kamel hatem 4 years ago

    Thanks a lot Teacher!!!!

  • Emvolts 4 years ago

    snail method

  • Justin 4 years ago

    she pretty hot too

  • Cosmic Reality 4 years ago

    So many creeps in the comments

    • Solace Creat 3 years ago

      Meh. Either way, if you’re desirable, you get creeps; if you’re undesirable, you get nothing. I like being creeped on a lot more than being considered irrelevant, personally. And I get it from gay dudes all the time, too, since I’m shredded. I’m of a mind you tend to dislike what you don’t get and want what you don’t have. If you get creeped on all the time, you want to be ignored; if you’re ignored all the time, you want to get any attention at all. *shrug*

    • Egg 3 years ago

      @Solace Creat I completely agree with you, frankly.

    • Lokesh Lutchmeenaraidoo 3 years ago

      where? lol

    • Aluna Spider 3 years ago

      Who are you weirdos lmao

    • Na Zombie 2 years ago

      not me! I am a novice mathematician I love mathematics

  • luis jimenez 4 years ago

    I love you

  • Ribeirao 4 years ago


  • Manuel Gomez 4 years ago

    You looking madd goood lol jk , but tbh I learned a lot ๐Ÿ™‚

  • Joshua Tovar 4 years ago

    Thank you so very much Nancy! You brought back my love for Math.

  • Gabriel Redd 4 years ago

    your videos are good!

  • Quincy Grant 4 years ago


  • Vikrant Sawant 4 years ago

    Who is here to know how she is writing?

    • SydneyKate 4 years ago


    • Vikrant Sawant 4 years ago

      @SydneyKate so u are curious, right??

    • SydneyKate 4 years ago

      Vikrant Sawant haha yes!

    • Vikrant Sawant 4 years ago

      @SydneyKate from?

  • Senpai 4 years ago

    Instead of writing reverse, can you speak reverse๐Ÿ˜‚๐Ÿ˜‚

    • Excel Maths 3 years ago

      She ain’t writing reverse

    • tobiassssssssssss 3 years ago

      WOW such a funny comment !!!!!!!

  • sonalika sonalika here's 4 years ago


  • sonalika sonalika here's 4 years ago

    Thanks Nancy you will solve my problem

  • kaaylashae 4 years ago

    i thank you .

  • MHSN27 MHSN 4 years ago

    thank U (Nancy)

  • Venizelos Evangelos 4 years ago

    x * logx = 400 Do you know how to solve for x?

    • Mr One 4 years ago

      I have the same question ! …. so did you figure out how to solve it ???!

    • Butter Bubbles 4 years ago

      Venizelos Evangelos This is what I got. x (logx) = 400
      Logx^x (Using poser property) = 400
      x^400 = x.
      Idk if thatโ€™s right but I hope it is, Iโ€™m really trying to learn logarithms because Algebra II is hard ;(

  • happy dino 4 years ago

    you’re actually such a good teacher

  • Christian Onwuha 4 years ago

    Would have been much more easier if you could take everything step by step, instead of assuming that we all know what you are doing.

  • Joh Nobert 4 years ago

    looov u….

  • daniel felix silva 4 years ago

    Congrats ,, amazing vรญdeo !!!
    Do you have WhatsApp ?

  • danny trials 4 years ago

    Cant refuse the way you ask for a like!

  • joshua bowman 4 years ago

    You pause on certain things just long enough that I think you are going to stumble over words, but then you pull it off flawlessly. It’s like i’m trying to finish your sentence for you in my mind, but then it all gets smoothed over into a great explanation. Love the videos! Thank you very much!

  • str1xt 4 years ago

    I approve of a hot nerd.

  • Neelkanth Academy Karunesh Pandey 4 years ago

    Congratulations for ur 1000k subscriber

  • Paulo Constantino 4 years ago

    Please Nancy stop playing with my heart….. I love you now and without you I am nothing… Zero…Null….Void…..Please allow me to worship you as my Goddess ?

    • I'm a Mellark 4 years ago

      You’re gross.

  • Sher King 4 years ago

    I love your method to do

  • hans 4 years ago

    I can’t sleep. So I’ll watch some math videos.

  • B P 4 years ago

    Does loga3x-logax=3?

  • Amar Kumar 4 years ago

    Oo wow

  • Angel Eduardo 4 years ago

    Now I feel like learning algebra

  • Nelson Molsom 4 years ago

    Nice……..ilove explaination

  • Jiminlesmolbean _ 4 years ago

    Oof do you think you can make a video graphing logarithms?

  • Moรฑa Cristalina 4 years ago

    How she solved that equation? At 3:24

    • [R] 4 years ago

      EDM Lover
      Equalize the exponents and solve for x

    • Moรฑa Cristalina 4 years ago


    • [R] 4 years ago

      EDM Lover

  • Franco Ortiz 4 years ago

    Do you happen to know anything about machine learning?

  • Joshua Borden 4 years ago

    hey baby

    • I'm a Mellark 4 years ago


    • The BlackMace 2 years ago


    • Joshua Borden 2 years ago

      Arihant Nayyar your name sounds like my fart

    • The BlackMace 2 years ago

      @Joshua Borden You should go to a doctor.

  • Fuad Phenomenon 4 years ago

    ur the problem solver to my everything

  • ksungjin10 4 years ago

    Are you writing backwards or are you flipping the video?

  • maryam algaithi 4 years ago

    Good explanation ๐Ÿ’“. Appreciate your efforts

  • Edmund Castellanos 4 years ago


  • Carol Jackson 3 years ago

    You are more helpful than all the other videos that I watched. Thank you so much!

  • lesibe Thipe 3 years ago

    Thank you Nancy you really helped me with your video and i managed to pass my exam . I wish you could make Applied Math videos

  • Claire Heimbigner 3 years ago

    You’re a LIFE SAVER! Thank you!

  • Irving Castillo 3 years ago

    How do you do a log function with different bases, you have another video?

  • vijay kumar chaganti pati 3 years ago

    I think logarithms videos should taken by you Nancy madam.I think you will respond on this faster as possible.Your teaching is good or we can say the best.

  • RK Rahul Karki 3 years ago

    Oh my god, she was writing normally! She used a mirror mode to make the video comprehensible.
    5 months ago


  • Olives Olive 3 years ago

    โค๏ธโค๏ธโค๏ธ thank you very much!!!!

  • Johni Watermelon 3 years ago

    Fuck math.

  • Meenakshi Jain 3 years ago

    9:05 you have written that its -2 will be rejected but if you try solving
    Log2(-2) + log2(-4) you will get 3 … so i suppose both the answers should be considered. Btw you teach great maโ€™am.

  • kien trung 3 years ago

    I do not know why I’m here but I like it

  • Bhavik Upadhyaya 3 years ago

    Now I won’t fail my exam my professor goes over it so slowly it’s hard to understand him Thank you

  • meteor liu 3 years ago

    Beautiful lady makes fabulous videos!

  • Nely Silva 3 years ago

    Missed one day of school and now Iโ€™m so lost.

    • Kenny O 3 years ago

      Nely Silva feel yah

  • indigopeach 3 years ago

    What if the logs have different bases? How would you solve that?

    • D4vEOFF 3 years ago

      You just use the equality: log_b(a) = log(a)/log(b) for each log and then all the logs will have a common base. ๐Ÿ™‚ (I know you posted this a month ago.. Hope you don’t mind :D)

    • Leo Volont 3 years ago

      @D4vEOFF Hi D4. Yeah, change of Base. but then the problem is what to do from there. fore instance lets say that we start out with LOG baseA (B) = LOG baseC (D) using Change of Base to get everything to the default base of Whatever we get LOG B / LOG A = LOG D / LOG C now, that is where people get hung up. In just that form of Rationals composed of LOG/LOG their are no properties of LOGS that we can exploit. then the best we can do is try to simplify out A B C D in order to get cancellations. But yes, searching “solving logs with different bases” brings up a few videos.

  • SUBAIEE 3 years ago

    i finished my studies and graduated from university this year and for some reason that we all know i still come to watch your videos ๐Ÿ™‚

  • Kyle Kenan 3 years ago

    this was good work

  • Matths Wiz 3 years ago

    good work…..keep on

  • karim sayed 3 years ago

    Nancy 3.14

  • Stephanie Waldschmidt 3 years ago

    Studying for my final and this helped a ton. Thank you so much c:

  • Muhammad Amir Altaf 3 years ago

    Log(-2) + log(-4) = 3, for this both sides are also equal but you said that for x = -2 the equation doesn’t satisfy ?

    • Clei Jรบnior 3 years ago

      You’ll need complex numbers to prove/solve “negative log”.

  • Momma Bear 3 years ago

    Thank you for the help!

  • Raya Kelley 3 years ago

    Math just becomes nature ๐Ÿ™‚

  • Yvonne Cross 3 years ago

    you saved my life thank you so so much

  • The brokeStudent 3 years ago

    fanh r u writing backwards๐Ÿค”๐Ÿค”…but love u thou

  • Bollywood channel 3 years ago

    Very nice

  • Edwiner 3 years ago

    I have an exam tomorrow and my only studying were these videos,lets see how it goes๐Ÿ˜๐Ÿ˜‚

  • Keshav Raj 3 years ago

    Amazing ๐Ÿค—.love from INDIA

  • Dindoo Nuffin 3 years ago

    I came here to find out how many logs it takes to make a raft. And stayed for teacher.

  • Tin 3 years ago

    Like? I love it! +1 sub.

  • Annmarie Powell-Brooks 3 years ago

    Good job!

  • Alexandre Vitoria 3 years ago

    I love this beautiful teacher.

  • Lygirf Oisaca 3 years ago

    a word thank u is never enough, ur videos are very helpful. so thank u to the exponent of infinity ๐Ÿ™‚

  • Rion 3 years ago

    Thanks for the video. Logarithms are interesting, although confused sometimes

  • Our World 3 years ago

    Youโ€™re amzinh

  • J D 3 years ago

    Love Love love the videos

  • Curious Case 3 years ago

    With each new video… I’m falling in love with you Nancy. I wish, back then during my school days I found someone like you. Excellent! ๐Ÿ˜Š ๐Ÿ™

  • Stefan Rลฑsz 3 years ago

    Unbelievable. ๐Ÿ˜

  • Finzz 3 years ago

    I don’t understand until you…. It pass exam 19/20 thank you so much.

  • Ltbo 67 3 years ago

    awesome video. great teacher thanks

  • chrisphaeton 3 years ago

    So helpful and clear. Thank you

  • Catherine Collins 3 years ago

    Wow thankyuhhh!!!!!!

  • Timothy Parker 3 years ago

    Log base2 (-2)(-4) = Log base2 (8)=3

  • Shilcom Technologies 3 years ago

    nyc if only you were my tutor

  • Dennis Rendfrey 3 years ago

    Again Thank You!! It’s Sunday morning and (I Do Like Math) my next semester (pre-calculus class is getting closer. With your help I will be ready. I just want to have an understanding of what my professor will be talking about.

  • Daniel Jabor 3 years ago

    I have to say you are looking cute and your math explanation are extremely awesome

  • Naomi Johnson 3 years ago

    Excellent explanation of logarithms.

  • Solace Creat 3 years ago

    I could listen to Nancy all day long. Alas, I haven’t gotten to quadratics yet, so I got lost. It was fun to see a bit into the future, though. I kinda like logs. Now back to finding the average rate of change of a function from a table over an interval. Grrrrrrr.

  • Wolfy Boi 3 years ago

    That part where she said “can’t unsee that” XD

  • Joneber Josh Japona 3 years ago

    Very much helpful.. Thanks

  • Vinod Kumar 3 years ago

    simply amazing…..why I haven’t came across this earlier ….great stuff…keep it ๐Ÿ‘Š๐Ÿ‘Šโœโœ

  • i am comedy 3 years ago

    Thank you!!!
    Really thank you!!

  • TushDeMort 3 years ago

    How do u write in MIRROR dude

    • Eduardo Galdino 3 years ago

      Mirris in back…

    • Eduardo Galdino 3 years ago


  • Eduardo Galdino 3 years ago

    Hey nancy, when the ekarts transdimentioned here ,they told me obviously we are not alone,,is that true?kkkk

  • Ruff Rider 3 years ago

    Logarithm are nothing but multiplication and division of numbers = how many times I have to do X to get to Y or How many Y does it take in X

  • Vincent Ortega 3 years ago

    Thanks Nancy, this helped so much. Your an Awesome teacher.

  • Daniela Barragan Cortazar 3 years ago

    you should do graphing log function

  • incredible TAWANG 3 years ago

    My best math faculty on YouTube.

  • Alberto Cayente Junior 3 years ago

    what if theres 2 logs (2logs=1log)


      Alberto Cayente Junior just simplify the 2 logs๐Ÿ˜‚๐Ÿ˜‚

  • NARKFLY 3 years ago

    could pause this video at any point and she still looks gorgeous, huh-dayum!!!

  • beverly francis 3 years ago

    LOL. Nancy story. Thanks.

  • Mel Bar 3 years ago

    I was stuck on a homework math problem for a while now and your video really helped me understand the rest of my homework!! Thank you so much and bless kind souls such as yourself for making math videos to help out others <3

  • Germaniaceez TV 3 years ago

    How does she write inverted?

  • Bobby Poly 3 years ago

    Thank you for making the bitter, sweet!!

  • lushin burl 3 years ago

    I don’t even go to school, but I can’t stop watching these videos. I think I’m falling in love with math. ( Or NancyPi). Lol

  • whats missing from A_SCHWITZ ?____ ANSWER: U 3 years ago

    2:22 “now i’m going to give you a whole meal”
    – sorry, I’m on a diet.

    • Mr. Singh 3 years ago

      bruhhhhhhhhhhhhh i never miss free meal …….no matter whattttttt

    • whats missing from A_SCHWITZ ?____ ANSWER: U 3 years ago

      @Mr. Singh same bro same

  • khatab omar 3 years ago


  • Alex Bravo 3 years ago

    Thank you , dear Nancy girl .. Excellent ! .. Very helpful indeed … ๐Ÿ™‚

  • Samim 3 years ago


  • honeybee2145 3 years ago

    You don’t have to wait for the tutor to write on the board. It is automatically fast forwarded for you . It will certainly saves you time. She is a very effective teacher. Thumbs up for her.

  • Mr. Singh 3 years ago

    11:15 when she speed ups the writing part….see in 0.25 speed… is still too fast …it means u waste a lot of time on that for us……aaaaaaammmmmmmmmmm very thankfullllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll tuuuuuuuuuuu juuuuuuuuuuuu

  • Adana Jackson 3 years ago

    If it wasn’t for your video help, I would most definitely have failed my math class! You’re the best tutor. Thank you for your videos! I only wish I had known they existed a little sooner!

  • Veritas et Aequitas 3 years ago

    Saves so much time vs Khan. Sal trying to explain multiplying logs was a nightmare.
    Also, she FF through through writing where Sal.. repeats himself.. repeats.. repeats… Himself… Himself… Himmm.. seeelf… Constantly because he doesn’t dare leave a moment not filled by his own voice.

  • Moletsane Violet 3 years ago

    she’s the best maths teacher ever โค๐Ÿ‘Œ

  • Nora 3 years ago

    ur very helpful but u talk too much, the video couldve been much shorter but other than that good work

  • steffy vi 3 years ago

    Thank you! You make everything seem so much more simple!!

  • Math Ventures 3 years ago

    Nancy could you please explain to me what a branch cut of the natural log is?

    Thatโ€™s what I thought you donโ€™t know… donโ€™t teach log if you donโ€™t really know it

    This chick aced an easy ass alg II class now she think she can teach everyone math ๐Ÿ˜‚

    • EverythingAndroid Ois 3 years ago

      Did ya hear she’s an MIT grad, she prob. had to do more than ace an Algebra II class, people make mistakes, random error.
      Don’t judge people like that, if you want to encourage her to do something do so politely. Good day.

    • Math Ventures 3 years ago

      She can be an MIT grad, she didnโ€™t make a mistake btw she actually doesnโ€™t even know what a log is. Going to mit doesnโ€™t mean anything if she only got a basic math education she could have gotten at a basic state university: if she wasnโ€™t hot no one would watch this.

  • Jesse chima 3 years ago

    I like maths, I like your videos and I like you. ๐Ÿ˜…

  • Aisha Mudashiru 3 years ago

    After my exam, I’ll make sure I watch all ur videos. You are just a life saver!

  • Zein Albasam 3 years ago

    Damn ur pretty

  • Jane Doe 3 years ago

    Stop scaring me >3<

  • Hema Manral 3 years ago

    Thank you Nancy pi it helped love you from india
    I didn’t knew maths tutor were good looking too

  • mitch & elle 3 years ago

    This video is great! It is so easy to understand and I really needed to know this for my math final exam :3

  • Alexandria Razon 3 years ago


  • 1815 2SC 3 years ago


  • Angel Morales 3 years ago

    Mire ha mi yo tengo halgo ke exponer sobre Hoyente ha distansia local interviene X cuantas honbre y cuantas mujer un maximo de tres los otros son primo EL mujer x el corbata no igual de cuerpo no es igual a un honbre las matematicas no entendibles sin ofisina de ufolojia pero si guardia sin ofisina misterio

  • ุฅุจุฏุงุน EBDAA 3 years ago

    I need help to solve this. Log3 (X) =X-2. What the value of X

  • Ricardo Saavedra 3 years ago

    Que linda la explicaciรณn

  • abdul aziz 3 years ago

    So smart n beautiful โ˜บ๏ธ from Indonesia

  • Hemakumar Gantepalli 3 years ago

    Loving your videos.

  • John Smith 3 years ago

    She’s Smart As A Whip…..

  • pranav s 3 years ago

    Brilliant simple way of serene teaching

  • kss pqf 3 years ago

    Why is this rubbish in my recommendations also why does this video exist just look up log laws so you can pass your exam you’ll never use them again ever

  • Everything DJ Related 3 years ago

    This is what a good education feels like I guess…

  • Carson Gray 3 years ago

    U helped me clutch another math test out. Thank you again. ๐Ÿ™‚

  • Branden Soo 3 years ago

    ive never paid this much attention to math

  • Dalyssa Alexander 3 years ago

    You should do a video on how to expand and condense logarithms

  • Fat Man 3 years ago

    So recently my teacher showing us a video of hers in class and ngl, she became one of my favorite people. She is soooo smart and pretty.

    • desertheat4u 2 years ago


  • Nate Cator 3 years ago

    Seem like I need to watch the other vid lol

  • Nisar Ali 3 years ago

    which app you are using to make such wonderful lectures?

  • Brendan Best 3 years ago


  • Declan Condon 3 years ago

    You lowkey bad

  • p z 3 years ago

    good explanation and also you’ve work pretty good on video editing fast forwarding the simplification steps that’s really save tiny amount of time, it’s really is helpful ๐Ÿ™‚

  • Elite a20 3 years ago

    How do write in reverse

  • john redgs martin 3 years ago

    log 12x-7 how did u get the -3 lol just for confirmation ty

  • Tharun K 3 years ago

    God bless u mam

  • L G 3 years ago

    you explain things so clearly thaNK YOU!!

  • Almost Enlightened Alexander 3 years ago

    I guess every student has a crush on teacher at some point of time ๐Ÿ˜๐Ÿ™Œ

    • Ricky S 2 years ago

      I have a crush on my teacher. The problem is I’m home schooled! ONLY KIDDING!

  • ุญุณูŠู† ุงู„ุดุฃุฎูˆุฑูŠ 3 years ago

    But what if the base was negative also. Will there be an answer to a negative log?

  • levendlicht 3 years ago

    You’re the equivalent of e^iฯ€ + 1 = 0 ๐Ÿ™‚ I’m working on a mathematical model of certain DNA structures, and how they interact with other molecules, but sometimes it’s refreshing to go back to where everything seems nice, elegant and beautiful. I’m having some problems to reformulate certain Euler angles into the right set of differential equations… Could you write them out for me on your magic mirror? ๐Ÿ™‚

  • FBI 3 years ago

    Nancy you absolute genius

  • Master Saitama 3 years ago

    That was no use for me๐Ÿ˜” I got wrong vedio

  • Atheer alenazi 3 years ago

    Where are you Nancy ?!๐Ÿ˜ฉ

  • Tessa Gunderson 3 years ago

    this is the first time logs have actually made sense to me, also its nice to see a girl teaching these videos for once ๐Ÿ™‚

  • Tamiamay 3 years ago

    Thank you so much. This video was so helpful.

  • SimonShitStain 2 years ago

    how areyou going inside google

  • Hannes Camitz 2 years ago

    I would never have guessed that a tiny snail could do so much for the sake of math to my thick skull!

  • T-ZARC 2 years ago

    She out here saving grades in the middle of this corona pandemic

    • Kal Karlssen 2 years ago

      I learned nothing in online math

    • Noah Kim 2 years ago

      On god she is

    • forever SHAMPOO 2 years ago

      @man0z its definitely engineered, but are you proposing thousands are not dying? give me proof

    • man0z 2 years ago

      @forever SHAMPOO thousands die everyday dude, in case you forgot that death is a natural part of life. Here in the UK the doctor is not required to test for the virus, if a patient has influenza and pneumonia and is suspected of having covid 19 (remember a positive test is not required) then they are added to the covid 19 stats. In America doctors are incentivised to diagnose covid 19, $13,000 and $39,000 for putting someone on a vent, which has a high risk of killing them. If you need proof of this look on the ONS website, there’s plenty of videos on youtube of people pointing out the incentives. Watch this too
      In America the education and careers of doctors are tightly controlled by a private institute the AMA which was set up by Rockefeller. Since the corrupt mass media fabricates propaganda on behalf of the corrupt government then you do the math.
      If 9/11 and Iraqi WMDs didn’t wake you up to the abhorrent amount of corruption in media and government and this doesn’t either then I am afraid you are a lost cause.
      Here watch this

    • Beast Master 64 2 years ago

      @man0z are you joking or are you acc that stupid

  • Phucci 2 years ago

    Only if I had you as my math teacher years ago I would have loved instead of hated math!

  • Daniel DeLarosa 2 years ago

    Thank you so freaking much you just saved my junior year

  • Gerson Horaseb 2 years ago

    Thanks helpful

  • ํ”ผ์„œ 2 years ago

    I can watch this all day

  • Sohail Javed abbasi 2 years ago

    You are as beautiful as math nancy

  • Stefan Pratarelli 2 years ago

    Thankyou for this video

  • Soldier Sauce 2 years ago

    Bro I have a test in 5 minutes and this saved me thank you

  • Geeta Peter 2 years ago

    You are awesome Nancy !! Love the way you explain !

  • manpreet singh 2 years ago

    Hello mam what is base of log. If no base is given in log

  • Robert Valsi 2 years ago

    You are helping my Algebra 2 classes during this “home” schooling. You should make Nancy Pi t-shirts!

  • Nathan K 2 years ago

    anybody else doesnt know how she factored at 7:44

  • MegaDee911 2 years ago

    Thanks Nancy.

  • Uncle Joe 2 years ago

    I got here from an Allen Holdsworth concert.
    (Give me a like when you finally get it ;-)…. )

  • Rakesh Mahecha 2 years ago

    Pls make video on reading log table๐Ÿ™๐Ÿ™

  • Emir Sadฤฑker 2 years ago

    Solving logs are easier than watching them

  • Miloลก Miloลกeviฤ‡ 2 years ago

    I’m not interested in math,but I enjoy

  • skilz8098 2 years ago

    Nice video, but there’s is one more property of Logs that wasn’t mentioned and that is the change of base…

  • Na Zombie 2 years ago

    Great videos!!! I love how you explain the process of mathematics and thank you for making this video. I needed some reference on the power and quotient property. You are beautiful and smart!!

  • Gen Valencia 2 years ago

    Thank you!

  • The Scholar Mind 2 years ago

    You are so beautiful ma’am . Why didn’t youtube recomend this before, anyways you are very pretty

  • vianne agha 2 years ago

    thank you

  • talenttrading 2 years ago

    It’s a mess! you can’t unsee that. Nancy you are my favorite

  • M Math 2 years ago

    Send to me a message, since i want together with in paper, working

  • Alicia Fernandez 2 years ago

    This was SO helpful. Thank you!!

  • Dan SW 2 years ago

    07:52 how do you get (x-4)(x+2) ?

  • Konsep Dasar 2 years ago

    in my opinion, you need to add a condition so that the logarithmic equation has a real number solution.

  • Dusty Vanderson 2 years ago

    I just came to see her

  • madhu ranjan dev 2 years ago

    Nice explaination. Love from india

  • Butterscout Boy978 2 years ago

    Anyone notice next to extra answers she wrote wtf?๐Ÿ˜‚๐Ÿ˜‚โœŒ๏ธ

  • Shiv Patel 2 years ago

    thanks sister for your help!!!!!!!

  • Piyush Raj 2 years ago

    Your teaching skills are as beautiful as you.

  • jose amram 2 years ago

    Nice job, Nancy, you are a great teacher.

  • Daya Naudiyal 2 years ago

    Thank you ma’am ๐Ÿ˜Š

  • Valmon Diasf 2 years ago

    Thanks! You save me!

  • Me & My brother's with my family 2 years ago

    Can you explain thi again pls

  • lee Bruce 2 years ago

    pretty teacher

  • codecaine 2 years ago

    Great video

  • SUPERSAB 2 years ago

    i never listen in math class, i choose to learn off here

  • Flapjack McCoy 2 years ago

    I like picturing a snail on a log…solving math problems. This video is lumberjack approved.

  • sika sika 2 years ago

    You really good ma’am, I have always been struggling with understand logarithm and lost courage and interest but after watching this video, I am looking forward to better grades in my exams. Love from Namibia ๐Ÿ‡ณ๐Ÿ‡ฆ

  • Hey Ohh 2 years ago

    Funny, If you test the results (-2 and 4) of the 2nd problem on log2(x^2 + 2x) both work.
    Weird??? Maybe is just coincidence.

  • Lemuel Castillano 2 years ago

    Hi! can i attach the youtube link of your video to the self-learning modules of our department in order for the students to learn more from the contents of this video aside from the modules that will be distributed to them? Thanks a lot.

  • abdi rashiid 2 years ago

    You are so quick pls quiet bby

  • ELITE ROCKET 2 years ago

    she always seems shy lol

  • Arman Sydikov 2 years ago

    Do you do competitive programming?

  • Jeffrey Chavey 2 years ago

    Best math teacher

  • Mike Jouhari 2 years ago

    I already know all of this but cant stop listening to her! She is great!

Comments are closed.