How do you solve 45 = e^x ?

Dec 8, 2015

$x = \ln \left(45\right)$

Explanation:

By definition:
$\textcolor{w h i t e}{\text{XXX}} \ln a = c \Leftrightarrow {e}^{c} = a$
(memorize this)

So
$\textcolor{w h i t e}{\text{XXX}} {e}^{x} = 45 \Leftrightarrow \ln 45$

Using a calculator $\ln 45 \cong 3.81$