Laws of Logarithms: ln(x^r) = r·ln(x)

in hive-196037 •  7 days ago  (edited)

In this video I go over another logarithm law and prove that ln(x^r) = r·ln(x) where r is a rational number. In this proof I use derivatives and integrals as opposed to my earlier video which I proved using the definition of ln(x) as the inverse of the exponential function, e^x.

Download the notes in my video:!As32ynv0LoaIg4NW5DRdhWIqa5Sg0g?e=55CxXn

View video notes on the Hive blockchain:

Related Videos:

Natural Logarithmns Defined as Integrals: Introduction:
Laws of Logarithms: ln(x*y) = ln(x) + ln(y):
Laws of Logarithms: ln(x/y) = ln(x) - ln(y):
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem:
Inverse Functions - f-1(x) - An Introduction:
Logarithms and their Properties - An Introduction:
Natural Logarithms, Log base 10, and Some Examples Using Logs:

▶️ DTube
Authors get paid when people like you upvote their post.
If you enjoyed what you read here, create your account today and start earning FREE STEEM!
Sort Order:  

I don't always deal with logs of power functions but when I do I usually simplify the function using log laws ;)

View video notes on the Hive blockchain: