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

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.

[stanhart]

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[Kapoompahpeempahpoompah]

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

[SkillslliK]

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

[naghmez]

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 🙏🌿🌹

[n_madno]

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

[anupambordoloi]

Came across your video after almost 4 years. I must say this is by far the best video on Youtube explaining the laws of Logarithm.
Thank you so much ❤

[moshemaor]

Hello, I am not sure if many will agree with me, but one of the advantages of your lessons is that you talk alot, and dive to small details. From such a teacher it is easy to learn, Thanks.

[hemarajue]

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

[caperider]

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

[penguinlearning]

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

[alexispbm]

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 <3

[karolissad.]

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

[rumanfurqan]

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

[digitalkhannak]

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

[Titfortat]

Sir, your teaching is so perfect, cherish us more with your knowledge, we are lucky that we are getting this type of education at the tip of our hands because of technology, thank you so much. ❤

[mftuitioncenter]

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

[RupaDas-yhcy]

I started my BCA Course from last week but I was a Humanities student so I didn't had Maths with 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🥺☮💐

[georgebeckons]

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

[nmaluqman]

Your ideal explanations always impress me

[SevenNationArmy]

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