# How do you solve ln(x^7) − ln(x^2) = 5?

May 22, 2018

Use properties of logarithms to combine the two natural logs and then pull the exponent out front.

#### Explanation:

$\ln \left({x}^{7}\right) - \ln \left({x}^{2}\right) = 5$

$\ln \left({x}^{7} / {x}^{2}\right) = 5$

$\ln \left({x}^{5}\right) = 5$

$5 \ln \left(x\right) = 5$

$\ln \left(x\right) = 1$

$x = e$