What is the quotient rule of logarithms?

1 Answer
Amory W.
Sep 10, 2014

The answer is #log (a/b)= log a - log b# or you can use #ln (a/b)=ln a - ln b#.

An example of how to use this: simplify using quotient property: #log ((2^5)/(2^2))#

#=log (2^5)-log(2^2)#
#=5log2 - 2log2#
#=3log2#

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

#=log (4^2)-log(3^5)#
#=log(16)-log(125)#
#=log ((16)/(125))#

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