Solving Logarithmic Equations... How? (NancyPi)

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: • Logarithms... How? (Na...
Follow Nancy on Instagram: / nancypi
Twitter: / nancypi
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?" ( • Logarithms... How? (Na... ) 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: nancypi.com

Пікірлер: 796

  • @t_zarc
    @t_zarc4 жыл бұрын

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

  • @danieldelarosa4252

    @danieldelarosa4252

    4 жыл бұрын

    Fr

  • @Steezydlo

    @Steezydlo

    4 жыл бұрын

    haha ong

  • @mahas943

    @mahas943

    4 жыл бұрын

    frr, shes better at teaching than my teachers man

  • @kalkarlssen3491

    @kalkarlssen3491

    4 жыл бұрын

    I learned nothing in online math

  • @noahkim7804

    @noahkim7804

    4 жыл бұрын

    On god she is

  • @markzart33
    @markzart333 жыл бұрын

    So far through lockdown, Nancy Pi, is beyonf doubt the most articulate mathematician on KZread, taking the viewer through the process in baby steps so that you cab REALLY grasp what is going on. I wish my maths teachers had been a tenth as good as she is.

  • @NazriB

    @NazriB

    10 ай бұрын

    Lies again? Serie A Leader AMWF CAR

  • @laurathomas3394
    @laurathomas33945 жыл бұрын

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

  • @amanc9835

    @amanc9835

    4 жыл бұрын

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

  • @JesusGarza-cu2oz

    @JesusGarza-cu2oz

    4 жыл бұрын

    @@amanc9835 😂

  • @sirleo5103

    @sirleo5103

    3 жыл бұрын

    @@amanc9835 lmfao.

  • @sirleo5103

    @sirleo5103

    3 жыл бұрын

    I don't think it's Nancy's lessons they're paying attention to...

  • @vengeance6060

    @vengeance6060

    3 жыл бұрын

    Idiot

  • @andrienefrancis5696
    @andrienefrancis56965 жыл бұрын

    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 :)

  • @atall1669

    @atall1669

    2 жыл бұрын

    just in time before my final :D

  • @chloeyen3077
    @chloeyen30775 жыл бұрын

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

  • @LattoSan

    @LattoSan

    5 жыл бұрын

    Chloe Yen Thats so amazing

  • @ObsidianParis

    @ObsidianParis

    5 жыл бұрын

    Nonsense, she's just applying the [ -1 0 ; 0 1 ] matrix by heart to her writings ! :-)

  • @KermitDominicano

    @KermitDominicano

    5 жыл бұрын

    or maybe just maybe she’s a god

  • @KermitDominicano

    @KermitDominicano

    5 жыл бұрын

    nah it’s mirror mode

  • @MajesticGamer1133

    @MajesticGamer1133

    5 жыл бұрын

    When ur an MIT grad......

  • @paulmaggiar8274
    @paulmaggiar82742 жыл бұрын

    Nancy, your videos are a pleasure to watch. I love the way you use a glass board, write clearly on it, and fast forward the writing. Your explanations are on point and you are also such an affable person. Thank you for all your help.

  • @rafoldstarking3715
    @rafoldstarking37155 жыл бұрын

    NancyPi. Your explanation is so efficient and elegant. I’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.

  • @ccsvenezuela2006
    @ccsvenezuela20065 жыл бұрын

    I never closed Khan Academy so fast :-)

  • @DecafMathASMR

    @DecafMathASMR

    5 жыл бұрын

    lol!

  • @jyl123

    @jyl123

    5 жыл бұрын

    ccsvenezuela2006 ha

  • @shy26gaming81

    @shy26gaming81

    5 жыл бұрын

    what?

  • @topones6879

    @topones6879

    5 жыл бұрын

    lol

  • @HowtoDoStuffwithEthan

    @HowtoDoStuffwithEthan

    5 жыл бұрын

    same

  • @joshuabowman6240
    @joshuabowman62405 жыл бұрын

    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!

  • @joshreilley540
    @joshreilley54011 ай бұрын

    I struggled for hours on this subject, but the way you break everything down is super helpful, I am finally starting to understand Logarithmic Equations.

  • @caroljackson767
    @caroljackson7675 жыл бұрын

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

  • @clarkgrayhame1250
    @clarkgrayhame12505 жыл бұрын

    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.

  • @tessagunderson8053
    @tessagunderson80534 жыл бұрын

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

  • @DanniWearsPrada
    @DanniWearsPrada5 жыл бұрын

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

  • @EFLO3D

    @EFLO3D

    5 жыл бұрын

    figuratively

  • @joshcuneo2782

    @joshcuneo2782

    4 жыл бұрын

    Eflo maybe they meant literally

  • @joshuatovar6298
    @joshuatovar62985 жыл бұрын

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

  • @neoblackcyptron
    @neoblackcyptron2 жыл бұрын

    An excellent teacher. Teaching is a gift, not everyone has that gift. This lady has the gift to convey ideas in a simple manner.

  • @Catanddoglover-mf9cz
    @Catanddoglover-mf9cz3 жыл бұрын

    I love how you waste no time with the writing but still explain it in a way someone can understand it. I normally don't have the patience for all of the writing and tend to skip and end up missing important notes for the lessons. Thank you for you well planned lessons.

  • @augustineyarngo6797
    @augustineyarngo67973 жыл бұрын

    Hello Nancy, This Terrence Yarngo, who watched your youTube video for personal studies of calculus daily. You are a great teacher and I admired your methods of teaching calculus, and logarithms using both the chain and product rules. The process you use to solve problems, makes calculus much more easier to understand. Please keep up the wonderful work you're doing for student like me. Thank you so very much for such an outstanding job! Best regards, Terrence Yarngo

  • @melbar4734
    @melbar47344 жыл бұрын

    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

  • @anamuniz8653
    @anamuniz86532 жыл бұрын

    thank you so much!!! this is the best video I have been able to find on logs! I love the way you explain and write everything so neatly!

  • @latoyamcintosh3903
    @latoyamcintosh39032 жыл бұрын

    Omg I’m studying for a major exam that requires math ( algebra, geometry etc) that I haven’t used in years and I could not get this in the review class and now I totally get it. You are a lifesaver. Thank you sooooo sooooo much for doing these videos. You really are making a difference to help struggling students like myself understand math. Again thank you and I appreciate you.

  • @saviimagnificent2099
    @saviimagnificent20995 жыл бұрын

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

  • @stefvi
    @stefvi4 жыл бұрын

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

  • @honeybee2145
    @honeybee21454 жыл бұрын

    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.

  • @pzingano
    @pzingano3 жыл бұрын

    Nancy has a magic touch, she explains very well, making mathematics more accessible to all. Complimenti!

  • @whosMandoo
    @whosMandoo5 жыл бұрын

    You’re literally a godsend Nancy!!! Thank you so much 🤞🏽💕 time to pass this math 41 final

  • @happylad7549

    @happylad7549

    3 жыл бұрын

    41%😂😂🔥

  • @eltonlucien4280
    @eltonlucien42805 жыл бұрын

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

  • @senzekilesibiya148
    @senzekilesibiya1485 жыл бұрын

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

  • @joelacosta5584

    @joelacosta5584

    5 жыл бұрын

    Senzekile Sibiya sammeee

  • @ushygushy9316

    @ushygushy9316

    5 жыл бұрын

    Same 😔

  • @SmileyBoySaGaming

    @SmileyBoySaGaming

    5 жыл бұрын

    logs are ez dafuq do u mean

  • @kiyoponnn

    @kiyoponnn

    4 жыл бұрын

    @@SmileyBoySaGaming Agreed. For me trig is harder because of all the fucking memorising I have to do😭

  • @isavenewspapers8890

    @isavenewspapers8890

    2 ай бұрын

    @@SmileyBoySaGamingSorry we can't all be as smart as you, Einstein.

  • @cloudysensation8406
    @cloudysensation84062 жыл бұрын

    That was possibly one of the best math tutorials ever. Thank you ☺️🙏🏽

  • @iDancetoLive12
    @iDancetoLive125 жыл бұрын

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

  • @aliciafernandez3962
    @aliciafernandez39624 жыл бұрын

    This was SO helpful. Thank you!!

  • @Zena.2271
    @Zena.22713 жыл бұрын

    You are an amazing maths instructor. I took this lesson 20 year's before when I was high school. You know what, logarithm was one of difficulty lesson on that time for me.I wish to be your students. Because you game me a clear image of logarithm concept. Tnx

  • @nazombie7935
    @nazombie79354 жыл бұрын

    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!!

  • @eligroisman2478
    @eligroisman24785 жыл бұрын

    Explained beautifully, in a simple way.

  • @pattifarrugia4650
    @pattifarrugia46502 жыл бұрын

    Quick and to the point...Beautifully said!

  • @mikejouhari4628
    @mikejouhari46283 жыл бұрын

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

  • @sikamalakia5274
    @sikamalakia52744 жыл бұрын

    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 🇳🇦

  • @antoniocovelli6130
    @antoniocovelli61303 жыл бұрын

    Thank you very much for all your videos. I think you are very Creative, Dedicated, Passionate, Caring, Grateful, Innovative, Excited, Motivated, Resourceful and Determined

  • @ajacks1077
    @ajacks10774 жыл бұрын

    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!

  • @anantimelrifle7769
    @anantimelrifle77693 жыл бұрын

    She explains this better than my professor. He talks through a crappy earbud microphone and will not slow down for the life of him lmao.

  • @GooseCrack

    @GooseCrack

    2 жыл бұрын

    dude the mic fr

  • @mohammeddawd3758
    @mohammeddawd37585 күн бұрын

    Nanacy you are the best. Because you approach is simple and bright to understand.

  • @dennisrendfrey5636
    @dennisrendfrey56364 жыл бұрын

    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.

  • @gunzlez
    @gunzlez4 жыл бұрын

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

  • @frigylacasio239
    @frigylacasio2395 жыл бұрын

    a word thank u is never enough, ur videos are very helpful. so thank u to the exponent of infinity :)

  • @Luckystone211
    @Luckystone211 Жыл бұрын

    That was awesome, A good mathematician indeed! was able to recollect,and relearn once again with all forms of log in a single lecture, Thanks Mam! Thankyou for your time.

  • @aishamudashiru4215
    @aishamudashiru42154 жыл бұрын

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

  • @Meee..9383
    @Meee..93833 жыл бұрын

    Thank you soooo much 😭 tomorrow i have a logarithm exam and i couldn’t understand anything from my teacher’s explanation but you really helped me❤️

  • @vincentortega4284
    @vincentortega42844 жыл бұрын

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

  • @_wash
    @_wash3 жыл бұрын

    This helped me a lot, thank you so much !!❤️

  • @playtune9217
    @playtune92174 жыл бұрын

    simply amazing.....why I haven't came across this earlier ....great stuff...keep it 👊👊✍✍

  • @shashianand250
    @shashianand2502 жыл бұрын

    I watched the video twice once for understanding logs and the second time for her. I appreciate everything.

  • @angelaseleke8660
    @angelaseleke86605 жыл бұрын

    Thank you Nancy,you make maths fun for me

  • @sujiths3196
    @sujiths31964 жыл бұрын

    Brilliant simple way of serene teaching

  • @heyitsme4240
    @heyitsme42405 жыл бұрын

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

  • @sikeimmike
    @sikeimmike11 ай бұрын

    At 9:30, you can use log_a(b)+log_a(c) = log_a(bc). [Two logs of the same base added together have their arguments multiplied together] Therefore, log_2(-2)+log_2(-4) = log_2(-2x-4) = log_2(8) which is equal to 3 as 2^3=8.

  • @onthegolabel
    @onthegolabel5 жыл бұрын

    Such a wonderful video, Twas helpful. Thank you!

  • @TI_Ted
    @TI_Ted5 жыл бұрын

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

  • @C.Ggames17
    @C.Ggames174 жыл бұрын

    U helped me clutch another math test out. Thank you again. :)

  • @saranrajv3
    @saranrajv3 Жыл бұрын

    Amazing explanation, appreciate all your effort

  • @justachildofGod
    @justachildofGod Жыл бұрын

    Such a lifesaver. I learned none of these properties in class and I thought I was somewhat prepared. Now I think I know it all!

  • @Gadavillers-Panoir
    @Gadavillers-Panoir Жыл бұрын

    After watching all her videos i realised that she’s actually teaching something. 🥰

  • @seekpeace494
    @seekpeace494Ай бұрын

    Thank you! You make it look extremely easy! ❤

  • @sumanyuagrawal1854
    @sumanyuagrawal1854 Жыл бұрын

    Now that I have watched this video, I can sleep peacefully knowing that I am able to keep up with what is being taught at my advance Math class. THANK YOU SO MUCH NANCY, YOU ARE A SLEEP SAVER!

  • @biancabrown7279
    @biancabrown7279 Жыл бұрын

    im not even mad there's so many ads this lady explains everything with such ease. She deserves it

  • @jamescorbin5638
    @jamescorbin56385 жыл бұрын

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

  • @lesibethipe1075
    @lesibethipe10755 жыл бұрын

    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

  • @adittyasakline5452
    @adittyasakline54523 жыл бұрын

    thank you, you explained these things so well

  • @tamiamay6722
    @tamiamay67224 жыл бұрын

    Thank you so much. This video was so helpful.

  • @addieb2453
    @addieb24533 жыл бұрын

    i've learned more in from you 15 minutes than i have in my entire 12 years of schooling. you are a lifesaver

  • @rodrigorodrigo7289
    @rodrigorodrigo72893 жыл бұрын

    Another excellent presentation!

  • @amramjose
    @amramjose4 жыл бұрын

    Nice job, Nancy, you are a great teacher.

  • @robertvalsi3948
    @robertvalsi39484 жыл бұрын

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

  • @CC-bu7tu
    @CC-bu7tu5 жыл бұрын

    You're a LIFE SAVER! Thank you!

  • @tarashmuts6240
    @tarashmuts62402 жыл бұрын

    literally taught me more in this 1 video then my teacher has taught me in 2 weeks. thank you sm

  • @aphazmba5505
    @aphazmba55053 жыл бұрын

    Thank you. This is really going to help me for my Grade 12 Maths Exam Paper 1 Tomorrow

  • @mg-qi9en
    @mg-qi9en5 жыл бұрын

    Good explanation 💓. Appreciate your efforts

  • @josephacri6855
    @josephacri6855 Жыл бұрын

    Haven’t seen any recent videos,I hope you return and everything is ok with you,your very talented in what you do,and it’s great to learn from you,again I hope to see you returning real soon😊👍

  • @huielchan4175
    @huielchan41752 жыл бұрын

    love your teaching video. very informative and helpful.

  • @kefayathussain8955
    @kefayathussain89553 жыл бұрын

    You are doing great job..I really enjoying your explaination

  • @siuil2394
    @siuil23942 жыл бұрын

    Thank you so much Nancy Pi! You saved my life.

  • @donaldbarker6380
    @donaldbarker63802 жыл бұрын

    I am struggling with my Applied Calculus course at University and I found her videos. So far I have watched close to 20, even reviewing the basics,(Factoring, Exponential etc). It is finally clicking. It is me, or is NancyPi absolutely adorable?

  • @augustineaboateng9707
    @augustineaboateng97073 жыл бұрын

    You are truly a great teacher.

  • @nelysilva7489
    @nelysilva74895 жыл бұрын

    Missed one day of school and now I’m so lost.

  • @kennyo4230

    @kennyo4230

    4 жыл бұрын

    Nely Silva feel yah

  • @calvinmead7564

    @calvinmead7564

    3 жыл бұрын

    For real. You could be doing nothing in school all week, then you miss one day and come back and missed this

  • @tomruss2477

    @tomruss2477

    2 жыл бұрын

    Literally me missing the first day of log

  • @britneyazuara1599

    @britneyazuara1599

    Ай бұрын

    MEEE LOL RN

  • @curiouscase
    @curiouscase4 жыл бұрын

    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! 😊 🙏

  • @arianaakhoundzadeh3328
    @arianaakhoundzadeh33283 жыл бұрын

    Thank you so so much for making me fall in love with math!!! God bless you xxx

  • @swiss4ever93
    @swiss4ever934 жыл бұрын

    Thank you for making the bitter, sweet!!

  • @johnmorrall2717
    @johnmorrall27173 жыл бұрын

    Excellent explanation Nancy

  • @denethrangana7419
    @denethrangana74192 жыл бұрын

    Creative level 100%. Thanks. Love you.❤

  • @nikolastesla8787
    @nikolastesla87872 жыл бұрын

    thanks for this informative video nancy

  • @karinadeleon7138
    @karinadeleon71385 жыл бұрын

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

  • @EklavyaGoyal

    @EklavyaGoyal

    5 жыл бұрын

    Lmao same

  • @leovolont

    @leovolont

    5 жыл бұрын

    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

  • @gregedwards9901
    @gregedwards99015 жыл бұрын

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

  • @peterbyrne6394
    @peterbyrne6394 Жыл бұрын

    Thank you. Very understandable explanation.

  • @okiadventure6031
    @okiadventure60312 жыл бұрын

    Wonderful! Thanks for the help

  • @fammy3241
    @fammy32413 жыл бұрын

    You're teaching style is so good.. I wish my teacher taught me like this.. Tysm for clearing all my doubts regarding logs 🙏❤

  • @wademckenzie3623
    @wademckenzie36235 жыл бұрын

    Thank You NANCY!!!!!!

  • @aleisiathomas49
    @aleisiathomas492 жыл бұрын

    I wish she did change of base because the ones on other channels are confusing me, and so far her channel is the best .

  • @ahmedsamy6798
    @ahmedsamy67982 жыл бұрын

    Clear, Helpful and Charming !, Thanks

  • @Yaboiignis
    @Yaboiignis3 жыл бұрын

    Great video! Really helping me out with my final tomorrow :^)

  • @chrisphaeton4762
    @chrisphaeton47624 жыл бұрын

    So helpful and clear. Thank you

  • @naomihjohnson
    @naomihjohnson4 жыл бұрын

    Excellent explanation of logarithms.