# How do you solve ln8-ln(x+4)=1?

Aug 21, 2016

$x = \frac{8}{e} - 4 = - 1.057$

#### Explanation:

$\ln 8 - \ln \left(x + 4\right) = 1$ can be written as

$\ln 8 - \ln \left(x + 4\right) = \ln e$ or

$\ln \frac{8}{x + 4} = \ln e$ or

$\frac{8}{x + 4} = e$ or

$x + 4 = \frac{8}{e}$

i.e. $x = \frac{8}{e} - 4$ or

$x = 2.943 - 4 = - 1.057$