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
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
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,
Electrical Engineer here. This is the best teacher I ever had.
@tomsdailystudy
Жыл бұрын
YUP!
@user-ue7rw4dj2v
Жыл бұрын
Here is an another agreeing electrical engineer
@eleftheriosgrillakis4814
9 ай бұрын
So true
what a step by step masterpiece over the technicality of this proof, loved it with your smooth explanation.
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
3 жыл бұрын
Awww thank you so much!
The entire English dictionary doesn't have enough word for me to express my gratitude to kind sir. God bless you sir
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
Another great video. Teaching maths online is the way to go!
@MathAndScience
3 жыл бұрын
I appreciate it!
Great expanations. Really helped me link the laws of logarithms and the laws of exponentials together!
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
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
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!
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
Your ideal explanations always impress me
You are an EXCELLENT teacher!
you are brilliant thanks so much. been waiting for this for so long
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
3 жыл бұрын
Yes!
@josuequintero-td5gh
4 ай бұрын
That's the same proof but with an extra step
EXCELLENT WAY OF EXPLAINING
Ohh that blank canvas description of a proof reminded me so much of Paul Lockharts "a mathematitians lament"!
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🙏..
Exceptional Teacher. Thank you so much Sir .
9th student here you are the best teacher in the world
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
3 жыл бұрын
Thanks Ryan! I’m so happy you are excelling in your studies! Jason
Great video!!!
I had 2 questions that directly asked to prove the log rules , lucky enough I watched this clip before the exams , thanks veeeeery much
U need recognition 🙏🙏
Thank you. I love it.
It's soo good..thanku so so much !! I was so confused in solving them but now I got it..
what a great teacher
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
2 жыл бұрын
Welcome!
Really cool to see the equations explained for the first time!
@MathAndScience
Жыл бұрын
Thank you!
very useful, thanks
Great work teacher
@MathAndScience
3 жыл бұрын
Thank you!
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
Жыл бұрын
I can feel it
Thank you very much Sir
Really Nice
Thanks a lot Sir ☺️.
Thank you sir
So glad you are helping thousands of students.keep it going .
@MathAndScience
Жыл бұрын
Thank you, I will!
thanks very much for this useful explaning I was searching alot until I found you ❤
Thank you say it's really helpful for my test.😇😇😇
Thanks teacher 🙏🙏🙏
Sir your speaking is very nice
Brilliant ✍🏻
Thanks Sir!
@MathAndScience
3 жыл бұрын
So happy you liked it! Jason, MathAndScience.com
Top teacher
Nice explain
Thanks!
@MathAndScience
7 ай бұрын
Thank you so very much!!
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.
i am from pakistaan but i understand you very well ang best explanation
Explaining IS TOO LONG .BUT THE WAY YOU TEACH IS GOOD.
Very nice explanation sir
@MathAndScience
3 жыл бұрын
Welcome! Jason, MathAndScience.com
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.
Thank u
תודה רבה לך אתה מורה מדהים
You are my sensei
thanks sir my all doubt clear
you saved my life
You are the best
I like your vedios because your mathod is good.
@MathAndScience
3 жыл бұрын
Thank you so much!
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 ❤
Interesting
Wow, I'm going to watch this many times. To get used the verbage and function.
Thank you so much sir love from nepal🇳🇵🇳🇵🇳🇵🇳🇵❣️
Thannnk you😅
beautiful
Good videoooo!!!
@MathAndScience
3 жыл бұрын
Thanks so much!
👍👍👍👍👍👍👍👍
Only these three proofs are available everywhere. I request you to prove the rest of the properties
blessed
nice
@MathAndScience
Жыл бұрын
Thanks
واي من الترجمة السريعة
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
6 ай бұрын
Bro 😂
@wannabe_scholar82
6 ай бұрын
@@Cloudx77Lmfao I forgot abt this shi 😂😂😂
spm 2022 hadir
Nice explanation but maths got me crying 😃
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
What's his instagram? I'd like him to help me with some solvings.... I have an exam in January
15:05 where did 1 disappeared 😳 or you dont write 1logbN
@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
If log_a^x=N Prove that, a^N=N
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
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
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.
🌟🌹🌟
May allah bless you
Anyone watch this video in class 11😂
...Q.E.D....
‘Mathematically legal’ haha
@greggaygayakutami1402
3 жыл бұрын
Not as legal as lewding a lol- Okay nvm
Like math voo-doo
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
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
Only these three proofs are available everywhere. I request you to prove the rest of the properties