# How do you solve log₃x² - log₃(2x) = 2?

Jan 15, 2016

x = 18

#### Explanation:

using the law of logs that : logx - log y = log$\left(\frac{x}{y}\right)$

$\Rightarrow {\log}_{3} {x}^{2} - {\log}_{3} 2 x = {\log}_{3} \left({x}^{2} / \left(2 x\right)\right) = {\log}_{3} \left(\frac{x}{2}\right)$

using the relationship : log_b a = n rArr a = b^n

then ${\log}_{3} \left(\frac{x}{2}\right) = 2 \Rightarrow \frac{x}{2} = {3}^{2} = 9 \Rightarrow x = 9 \times 2 = 18$