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What is the quotient rule of logarithms?

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Sep 10, 2014

The answer is $log (\frac{a}{b}) = log a - log b$ $log (a/b)= log a - log b$ or you can use $ln (\frac{a}{b}) = ln a - ln b$ $ln (a/b)=ln a - ln b$ .

An example of how to use this: simplify using quotient property: $log (\frac{2^{5}}{2^{2}})$ $log ((2^5)/(2^2))$

$= log (2^{5}) - log (2^{2})$ $=log (2^5)-log(2^2)$
$= 5 log 2 - 2 log 2$ $=5log2 - 2log2$
$= 3 log 2$ $=3log2$

Or you could have a problem in reverse: express as a single log: $2 log 4 - 3 log 5$ $2log4 - 3log5$

$= log (4^{2}) - log (3^{5})$ $=log (4^2)-log(3^5)$
$= log (16) - log (125)$ $=log(16)-log(125)$
$= log (\frac{16}{125})$ $=log ((16)/(125))$

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