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: https://1drv.ms/b/s!As32ynv0LoaIg4NW5DRdhWIqa5Sg0g?e=55CxXn

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/laws-of-logarithms-ln-x-r-r-ln-x

Related Videos:

Natural Logarithmns Defined as Integrals: Introduction: http://youtu.be/M-N2PQ5UZns
Laws of Logarithms: ln(x*y) = ln(x) + ln(y): http://youtu.be/2SCZzFy2b2s
Laws of Logarithms: ln(x/y) = ln(x) - ln(y): http://youtu.be/GXkyY9EmDGM
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk
Inverse Functions - f-1(x) - An Introduction: http://youtu.be/qIqj3oKwFi8
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Natural Logarithms, Log base 10, and Some Examples Using Logs: http://youtu.be/XRSkMk5L3pk


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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: https://peakd.com/hive-128780/@mes/laws-of-logarithms-ln-x-r-r-ln-x