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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