# How do you expand log ((x^4)/(x-2))?

May 25, 2016

$4 \log x - \log \left(x - 2\right)$

#### Explanation:

Remember logs are indices, so the same rules apply.
If you are dividing two numbers, (as in this case) then subtract their logs.

log[x^4 ÷ (x-2)] = logx^4 - log(x-2)
Using the power law:

$4 \log x - \log \left(x - 2\right)$