### To expand the logarithm (break it apart),rewrite multiplication as
the same base logarithm being added.

## log_{3}5x = log_{3}5 + log_{3}x

### To simplify the logarithm(put it together), if the logarithms have the same
base, keep the logarithm and base, and multiply the arguments together.

## log_{10}2 + log_{10}7 = log_{10}(2x7) = log_{10}14

### To expand the logarithm (break it apart),rewrite division as the same base logarithm being subtracted.

## log_{3}5/x = log_{3}5 - log_{3}x

### To simplify the logarithm(put it together), if the logarithms have the same
base, keep the logarithm and base, and divide the arguments.

## log_{10}12 - log_{10}3 = log_{10}(12/3) = log_{10}4

### To expand the logarithm (break it apart),rewrite exponents as factors in front of the logarithm.

## log_{3}5^{x} = xlog_{3}5

### To simplify the logarithm(put it together), if there is a factor out front, make it the exponent of the argument.

## 2log_{5}3=log_{5}3^{2} =log_{5}9