# How do you solve 8^x = .5?

Mar 12, 2016

We can use the logarithm to find $x = - \frac{1}{3}$

#### Explanation:

We start by observing that everything in the equation is a power of 2 and rewrite it as such

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

We can then collapse the power by multiplying the exponents

${2}^{3 x} = {2}^{-} 1$

Now we can take the ${\log}_{2}$ of both sides giving

$3 x = - 1$

finally

$x = - \frac{1}{3}$