# How do you solve 3^(x-4)= 27^(x+2)?

Jun 16, 2016

The answer is $x = - 5$

#### Explanation:

${3}^{x - 4} = {27}^{x + 2}$

First step is to write ${27}^{x + 2}$ as the power of $3$

${3}^{x - 4} = {3}^{3 \left(x + 2\right)}$

Now you can write this equation as the equation of exponents:

$x - 4 = 3 \left(x + 2\right)$

$x - 4 = 3 x + 6$

$x - 3 x = 6 + 4$

$- 2 x = 10$

$x = - 5$