# How do you solve 2^(2x-1) = 8^(x+7)?

Sep 4, 2016

$x = - 22$

#### Explanation:

We have: ${2}^{2 x - 1} = {8}^{x + 7}$

Let's express the right-hand side in terms of $2$:

$\implies {2}^{2 x - 1} = {\left({2}^{3}\right)}^{x + 7}$

Using the laws of exponents:

$\implies {2}^{2 x - 1} = {2}^{3 x + 21}$

$\implies 2 x - 1 = 3 x + 21$

$\implies x = - 22$