Laws of Logarithms: ln(x^r) = r·ln(x)
4,668 views · Published 21 April 2014 · 5:07 · Indexed 21 September 2026
Channel: Math Easy Solutions · 2014 · Education
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 . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps
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