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

Jun 25, 2017

$x = \frac{5}{2}$

#### Explanation:

$\text{express the left side in "color(blue)"base 2}$

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

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

$\text{since the bases are equal we can equate the exponents}$

$\Rightarrow 3 x - 3 = x + 2$

$\Rightarrow 2 x = 5$

$\Rightarrow x = \frac{5}{2}$