# How do you solve e^(x-2) = 5?

Feb 26, 2016

$x = 2 + \ln 5 = 3.6094$

#### Explanation:

Take the natural logarithm on both sides and use the laws of logs to obtain

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

$\therefore \left(x - 2\right) \ln e = \ln 5$

$\therefore x = 2 + \ln 5$

$= 3.6094$