# How do you solve 3^x=500?

Mar 30, 2018

$x = \frac{\log \left(500\right)}{\log \left(3\right)}$

#### Explanation:

First, take the $\log$ of both sides of the equation to get:
$\log \left({3}^{x}\right) = \log \left(500\right)$

Then use the logarithmic power property to eliminate the exponent:
$x \log \left(3\right) = \log \left(500\right)$

Finally, divide both sides of the equation by $\log \left(3\right)$:
$x = \frac{\log \left(500\right)}{\log \left(3\right)}$