# How do you solve ln(x+8)-ln7=3?

Aug 5, 2016

$x = 7 {e}^{3} - 8 \cong 132.6$

#### Explanation:

$\ln \left(x + 8\right) - \ln 7 = 3$

Since $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$

$\ln \left(x + 8\right) - \ln 7 = \ln \left(\frac{x + 8}{7}\right)$

Since $\ln a = b \to a = {e}^{b}$
Our equation can be written as: $\frac{x + 8}{7} = {e}^{3}$

Hence: $x + 8 = 7 {e}^{3}$

$x = 7 {e}^{3} - 8 \cong 132.6$