# How do you solve log_17(9-n)=log_17(-4n)?

Jul 16, 2016

n = -3

#### Explanation:

Using the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\log x = \log y \Rightarrow x = y} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This applies to logarithms to any base.

$\Rightarrow 9 - n = - 4 n \Rightarrow n = - 3$