06 - Proving the Logarithm (Log) Rules - Understand Logarithm Rules & Laws of Logs

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Twitter: / jasongibsonmath
In this lesson, we will discuss at great length the logarithm laws that are used in all branches of math, science, and engineering. First, we will write down these log rules. Next we will construct a logical step by step proof of each logarithm law. At the end of the lesson, you will understand why, for example, addition of logarithms can be written as a multiplication. These laws of logs are used in higher math courses such as calculus, differential equations, and beyond because they lay the foundation for more complex problems.

Пікірлер: 114

  • @stanhart705
    @stanhart7057 ай бұрын

    You have perfected the Art of teaching. I'm recovering from back surgery and have lots of time. I can't get enough of your lectures. Many a night I have fallen asleep after watching hours upon hours. Then rewatch. I'm actually learning very useful information. My only problem is I'm now 71 years young. Keep up your good work. I will watch all of your videos. Stay safe!!!

  • @MathAndScience

    @MathAndScience

    7 ай бұрын

    This comment makes me so happy cheers to you friend across the Internet. I wish you the best of luck take care,

  • @Kapoompahpeempahpoompah
    @Kapoompahpeempahpoompah3 жыл бұрын

    Electrical Engineer here. This is the best teacher I ever had.

  • @tomsdailystudy

    @tomsdailystudy

    Жыл бұрын

    YUP!

  • @user-ue7rw4dj2v

    @user-ue7rw4dj2v

    Жыл бұрын

    Here is an another agreeing electrical engineer

  • @eleftheriosgrillakis4814

    @eleftheriosgrillakis4814

    9 ай бұрын

    So true

  • @SkillslliK
    @SkillslliK2 жыл бұрын

    what a step by step masterpiece over the technicality of this proof, loved it with your smooth explanation.

  • @naghmez5806
    @naghmez58063 жыл бұрын

    I can feel how you enjoy solving the problems and show they way to others. That's why it's always sooo sweet to listen to you and see how closed doors open to the light. God bless you 🙏🌿🌹

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Awww thank you so much!

  • @n0_madno916
    @n0_madno916 Жыл бұрын

    The entire English dictionary doesn't have enough word for me to express my gratitude to kind sir. God bless you sir

  • @digitalkhannak994
    @digitalkhannak99420 күн бұрын

    thank you so much, sir. I mean my teacher couldn't explain these proof questions to me I a whole lecture and u made it so easy and understandable in a matter of a few minutes. the explanation was so good and quick but smooth. ty

  • @penguinlearning450
    @penguinlearning4503 жыл бұрын

    Another great video. Teaching maths online is the way to go!

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    I appreciate it!

  • @SevenNationArmy12
    @SevenNationArmy122 жыл бұрын

    Great expanations. Really helped me link the laws of logarithms and the laws of exponentials together!

  • @caperider1160
    @caperider11603 жыл бұрын

    I get so entertained and relaxed when I see mathematical proofs. This short video was so pleasant to watch. Thank you. Ps: I took physics to graduate level and I am currently teaching my 16 yr old daughter HL IB MATHS in the midst of covid-19 pandemic

  • @nol2521

    @nol2521

    2 жыл бұрын

    I’m taking HL IB math next year, every time I get introduced to a topic in math I feel the need to look up proofs for rules I don’t understand because I HATE working with things I don’t understand. It’s sort of like being ashamed to use a tool I don’t deserve. Knowing why a rule works helps me use it in math problems while still being able to sleep at night lol

  • @bereadyforitsingh5359

    @bereadyforitsingh5359

    2 жыл бұрын

    Hey, I go to an IB school and will be taking IB Math AA next year, and I wanted know: how far will this content go? for example, will we go into integrals and diifferentiation of these functions, or even further? Thanks in advance!

  • @alexispbm
    @alexispbm2 жыл бұрын

    I have seen now quite some proof of these laws and I can say so far he has been the best in decribing them IMO

  • @nmaluqman3408
    @nmaluqman34083 жыл бұрын

    Your ideal explanations always impress me

  • @sukd2669
    @sukd26693 жыл бұрын

    You are an EXCELLENT teacher!

  • @omargrisha6019
    @omargrisha60193 жыл бұрын

    you are brilliant thanks so much. been waiting for this for so long

  • @hemarajue2736
    @hemarajue27363 жыл бұрын

    One of the purpose of our study is to develop independent thinking. Independent thinking leads to self development, creative thinking and less dependeny. It doesn't mean isolation but activation. I think we can also prove like this: let log MN=X b^x=MN Let M=b^y implies log M=y N=b^z implies log N=z MN=b^y.b^z= b^(y+z) i.e b^x=b^(y+z) Hence X=y+z log MN= log M+log N

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Yes!

  • @josuequintero-td5gh

    @josuequintero-td5gh

    4 ай бұрын

    That's the same proof but with an extra step

  • @AbdulManan-qb2gf
    @AbdulManan-qb2gf6 ай бұрын

    EXCELLENT WAY OF EXPLAINING

  • @karolissad.4270
    @karolissad.4270Ай бұрын

    Ohh that blank canvas description of a proof reminded me so much of Paul Lockharts "a mathematitians lament"!

  • @lukekari2084
    @lukekari20843 жыл бұрын

    Your teaching is very analytical and understandable for developing concepts of how programed mathematical situations has been derived from. This is very good 👍. I would reckon rate you 5🏅🏅🏅🏅🏅 or would gave you a 10/10 scale ⚖ . Very impressive.never seen a teaching like this..keep doing it. It helps people like me🙏..

  • @biswanathdutta6213
    @biswanathdutta6213 Жыл бұрын

    Exceptional Teacher. Thank you so much Sir .

  • @user-mz9bz2bl5p
    @user-mz9bz2bl5p6 ай бұрын

    9th student here you are the best teacher in the world

  • @rdjess
    @rdjess3 жыл бұрын

    Not related to this video, but wanted to let you know I subscribed to your website - and I credit you for my grades going up. If you’re struggling with any math/science subject, consider subscribing to his website. There’s tons of helpful videos. And no I’m not being paid to say this. 😂

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Thanks Ryan! I’m so happy you are excelling in your studies! Jason

  • @lux-nocopyrightmusic
    @lux-nocopyrightmusic8 ай бұрын

    Great video!!!

  • @mftuitioncenter
    @mftuitioncenter9 ай бұрын

    I had 2 questions that directly asked to prove the log rules , lucky enough I watched this clip before the exams , thanks veeeeery much

  • @dalitsotembo5912
    @dalitsotembo59122 ай бұрын

    U need recognition 🙏🙏

  • @taihatranduc8613
    @taihatranduc861310 ай бұрын

    Thank you. I love it.

  • @AJain20265
    @AJain202652 жыл бұрын

    It's soo good..thanku so so much !! I was so confused in solving them but now I got it..

  • @eddielaiche7345
    @eddielaiche73455 күн бұрын

    what a great teacher

  • @corono881
    @corono8812 жыл бұрын

    Thank you very much, sir! I have trouble using the simplest of rules without understanding the origins of them. This made the whole concept of logs 'click' for me, so once again; thank you so so much! /born again math-student

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    Welcome!

  • @georgebeckons539
    @georgebeckons539 Жыл бұрын

    Really cool to see the equations explained for the first time!

  • @MathAndScience

    @MathAndScience

    Жыл бұрын

    Thank you!

  • @qiqiliang7364
    @qiqiliang7364 Жыл бұрын

    very useful, thanks

  • @baraaktail6860
    @baraaktail68603 жыл бұрын

    Great work teacher

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Thank you!

  • @RupaDas-yh9cy
    @RupaDas-yh9cy Жыл бұрын

    I started my BCA Course from last week but I was a Humanities student so I didn't had Maths with me.....This sudden introduction to Maths made me worried a lot but you helped me and are helping me with Maths....Thank You so much for these amazing vids🥺☮💐

  • @sumitbhoi4070

    @sumitbhoi4070

    Жыл бұрын

    I can feel it

  • @rjsaha93
    @rjsaha932 жыл бұрын

    Thank you very much Sir

  • @arnavagrawal2673
    @arnavagrawal2673Ай бұрын

    Really Nice

  • @hudakaif
    @hudakaif2 жыл бұрын

    Thanks a lot Sir ☺️.

  • @aabbe762
    @aabbe762 Жыл бұрын

    Thank you sir

  • @rumanfurqan1097
    @rumanfurqan1097 Жыл бұрын

    So glad you are helping thousands of students.keep it going .

  • @MathAndScience

    @MathAndScience

    Жыл бұрын

    Thank you, I will!

  • @Amr-Monasser
    @Amr-Monasser10 ай бұрын

    thanks very much for this useful explaning I was searching alot until I found you ❤

  • @chinmoyee.....2944
    @chinmoyee.....29443 жыл бұрын

    Thank you say it's really helpful for my test.😇😇😇

  • @tocatikina9999
    @tocatikina99992 жыл бұрын

    Thanks teacher 🙏🙏🙏

  • @pudignaneswari3339
    @pudignaneswari3339 Жыл бұрын

    Sir your speaking is very nice

  • @Ammadrajput05
    @Ammadrajput05 Жыл бұрын

    Brilliant ✍🏻

  • @offside4l
    @offside4l3 жыл бұрын

    Thanks Sir!

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    So happy you liked it! Jason, MathAndScience.com

  • @Aijsz2
    @Aijsz2 Жыл бұрын

    Top teacher

  • @imransulaimani1515
    @imransulaimani1515 Жыл бұрын

    Nice explain

  • @stanhart705
    @stanhart7057 ай бұрын

    Thanks!

  • @MathAndScience

    @MathAndScience

    7 ай бұрын

    Thank you so very much!!

  • @Vegasbill80
    @Vegasbill80 Жыл бұрын

    I really like that when you learn a basic rule or concept. The first lesson should be how you derive it. Prove it first then you can use it. Try to get away with simply memorizing rules and formulas.

  • @saim-rc4bb
    @saim-rc4bbАй бұрын

    i am from pakistaan but i understand you very well ang best explanation

  • @MM-dj2cv
    @MM-dj2cv3 жыл бұрын

    Explaining IS TOO LONG .BUT THE WAY YOU TEACH IS GOOD.

  • @jayalakshmiviji7906
    @jayalakshmiviji79063 жыл бұрын

    Very nice explanation sir

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Welcome! Jason, MathAndScience.com

  • @agostinelliross
    @agostinelliross5 ай бұрын

    Soooo, basically look at a problem and see how you can rewrite a terms equivalen. Then assign a term to a variable. Then use laws/formulas of logarithms to further set your equation to the ptoof. Then set each side of equation to the terms needed in problem/proof given. The substitute equivalents in proof as needed b to solve.

  • @avani4740
    @avani4740 Жыл бұрын

    Thank u

  • @Royalord512
    @Royalord5122 ай бұрын

    תודה רבה לך אתה מורה מדהים

  • @xX_Dr_Suave_Xx
    @xX_Dr_Suave_Xx3 жыл бұрын

    You are my sensei

  • @GOLU-zg9cg
    @GOLU-zg9cg2 жыл бұрын

    thanks sir my all doubt clear

  • @BotKiller-xk3nw
    @BotKiller-xk3nw3 ай бұрын

    you saved my life

  • @Fili1113
    @Fili11133 жыл бұрын

    You are the best

  • @adnanashraf9002
    @adnanashraf90023 жыл бұрын

    I like your vedios because your mathod is good.

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Thank you so much!

  • @zohaali7924
    @zohaali792411 ай бұрын

    Okay wait a minute I am from Pakistan and lots of respect to you I didn't find any vedio from my country which can make me understand 😂 Thanks a lot ❤

  • @rinkumeena7240
    @rinkumeena72402 жыл бұрын

    Interesting

  • @agostinelliross
    @agostinelliross5 ай бұрын

    Wow, I'm going to watch this many times. To get used the verbage and function.

  • @rajendrakharel2998
    @rajendrakharel29982 жыл бұрын

    Thank you so much sir love from nepal🇳🇵🇳🇵🇳🇵🇳🇵❣️

  • @ralphkasumba3714
    @ralphkasumba3714 Жыл бұрын

    Thannnk you😅

  • @benny9794
    @benny97949 ай бұрын

    beautiful

  • @okayyyletsgooo7865
    @okayyyletsgooo78653 жыл бұрын

    Good videoooo!!!

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    Thanks so much!

  • @samoxguiseb977
    @samoxguiseb977Ай бұрын

    👍👍👍👍👍👍👍👍

  • @NoName-li4jo
    @NoName-li4jo2 жыл бұрын

    Only these three proofs are available everywhere. I request you to prove the rest of the properties

  • @orion_222
    @orion_2222 жыл бұрын

    blessed

  • @estherbassey9283
    @estherbassey9283 Жыл бұрын

    nice

  • @MathAndScience

    @MathAndScience

    Жыл бұрын

    Thanks

  • @ahmadsaeed5872
    @ahmadsaeed5872 Жыл бұрын

    واي من الترجمة السريعة

  • @wannabe_scholar82
    @wannabe_scholar82 Жыл бұрын

    Hey bro I rlly liked the video but next time can u try to be the screen a little less I couldn't see the notes but I love your shirt man!!! And loving the haircut 😁

  • @Cloudx77

    @Cloudx77

    6 ай бұрын

    Bro 😂

  • @wannabe_scholar82

    @wannabe_scholar82

    6 ай бұрын

    ​@@Cloudx77Lmfao I forgot abt this shi 😂😂😂

  • @afhamrafiq8188
    @afhamrafiq8188 Жыл бұрын

    spm 2022 hadir

  • @vanshitkhajuria8882
    @vanshitkhajuria8882 Жыл бұрын

    Nice explanation but maths got me crying 😃

  • @vijayakumarp7593
    @vijayakumarp75935 ай бұрын

    Nice video. I have subscribed to your channel. Need your help to prove " log (base x) N^ x = x " . Your response is highly appreciated. Thank you so much

  • @etzjunior_
    @etzjunior_3 жыл бұрын

    What's his instagram? I'd like him to help me with some solvings.... I have an exam in January

  • @manlikezakaado6135
    @manlikezakaado61352 жыл бұрын

    15:05 where did 1 disappeared 😳 or you dont write 1logbN

  • @cortiz8726

    @cortiz8726

    2 жыл бұрын

    yes he switched the 1/n into exponent because i know im late but, logb(1/n) = logb(N)^-1 so he rewrote the logarithm getting the exponent in front of the logarithm because alogb(x)=logb(x)^a. In this case the exponent was negative so it was -1logb(N), sorry im late lol

  • @abiabdullah2574
    @abiabdullah2574 Жыл бұрын

    If log_a^⁡x=N Prove that, a^N=N

  • @skillinjah5905
    @skillinjah5905 Жыл бұрын

    On the second law, why cant you take out the log on the left hand side the same as the right hand side, you explain that a log to a # with an exponent allows you to remove the log/# but only do it to one side??

  • @skillinjah5905

    @skillinjah5905

    Жыл бұрын

    9:22 thats where im lost, it just doesnt make any sense to leave the left hand side alone but remove the log from the right??

  • @MathAndScience

    @MathAndScience

    Жыл бұрын

    Look carefully on the right hand side. The log of the exponential cancel each other. This always happens when we are taking the log of an exponential if the bases are the same, because the log and exponential functions are inverses of each other.

  • @sammin5764
    @sammin57642 жыл бұрын

    🌟🌹🌟

  • @user-ue7rw4dj2v
    @user-ue7rw4dj2v Жыл бұрын

    May allah bless you

  • @RS.MVR43
    @RS.MVR433 ай бұрын

    Anyone watch this video in class 11😂

  • @benjaminhogan3157
    @benjaminhogan3157 Жыл бұрын

    ...Q.E.D....

  • @Aim4sixmeals
    @Aim4sixmeals3 жыл бұрын

    ‘Mathematically legal’ haha

  • @greggaygayakutami1402

    @greggaygayakutami1402

    3 жыл бұрын

    Not as legal as lewding a lol- Okay nvm

  • @agostinelliross
    @agostinelliross5 ай бұрын

    Like math voo-doo

  • @mihali_lifts
    @mihali_lifts Жыл бұрын

    can someone please explain to me why logb(b^x+y) cancels out logb(b) and leaves it with x+y i don’t quite get it😓, thank you in advance 🥹🥹🫶

  • @rupalinath4627

    @rupalinath4627

    Жыл бұрын

    Bro listen carefully Log b(b^x+y) in this the "b" which is in the base cancels the "b" in its power This is also a law of logarithm

  • @NoName-li4jo
    @NoName-li4jo2 жыл бұрын

    Only these three proofs are available everywhere. I request you to prove the rest of the properties