Question

What is the quotient rule of logarithms?

Answer 1

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))`