# How do you rewrite Log_3 8 - 4log_3(x^2) as a single log?

Oct 30, 2015

$- 8 {\log}_{3} 8 x$

#### Explanation:

By using laws of logs and exponents we get:

${\log}_{3} 8 - 4 {\log}_{3} {x}^{2} = {\log}_{3} 8 - 8 {\log}_{3} x$

$= {\log}_{3} 8 - {\log}_{3} {x}^{8}$

$= {\log}_{3} \left(\frac{8}{x} ^ 8\right)$

$= {\log}_{3} 8 {x}^{- 8}$

$= - 8 {\log}_{3} 8 x$

(Note: There might be other valid ways to express it as well)