Question

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

Answer 1

x = 18

Explanation:

using the law of logs that : logx - log y = log`(x/y)`

`rArr log_3 x^2 - log_3 2x = log_3 (x^2/(2x)) = log_3(x/2)`

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

then `log_3 (x/2) = 2 rArr x/2 = 3^2 =9 rArr x = 9 xx 2 = 18`