# How do you solve 7^x + 2 = 410?

May 20, 2016

3.09

#### Explanation:

${7}^{x} + 2 = 410$

${7}^{x} = 408$

Take the natural log of both sides,we get,

$\ln \left({7}^{x}\right) = \ln \left(408\right)$

Using logarithm properties, we can bring the x exponent outside the ln

$x \ln \left(7\right) = \ln \left(408\right)$

$x = \ln \frac{408}{\ln} \left(7\right)$

$= \left(6.0112\right)$/$\left(1.945\right)$

$3.09$