# How do you solve the exponential inequality 3^(x-2)<=3^(2x+4)?

Jun 13, 2017

Given: ${3}^{x - 2} \le {3}^{2 x + 4}$

Use the base 3 logarithm on both sides:

${\log}_{3} \left({3}^{x - 2}\right) \le {\log}_{3} \left({3}^{2 x + 4}\right)$

This makes both the logarithm and the 3 disappear:

$x - 2 \le 2 x + 4$

Subtract x from both sides:

$- 2 \le x + 4$

Subtract 4 from both sides:

$- 6 \le x$