# How do you solve 3.5^(5x) = 2650?

May 16, 2016

I found: $x = 1.2584$

#### Explanation:

We could first take the natural log of both sides:
$\ln {\left(3.5\right)}^{5 x} = \ln \left(2650\right)$
then get rid of the exponent in the first using a property of logs to write:
$5 x \ln \left(3.5\right) = \ln \left(2650\right)$
rearrange:
$x = \ln \frac{2650}{5 \ln \left(3.5\right)} = 1.2584$