# How do you solve 18=e^(3x)?

Dec 24, 2016

$x = 0.963 \left(3 s . f .\right)$

#### Explanation:

$18 = {e}^{3 x}$

convert into a logarithmic function:

e.g. ${\log}_{10} \left(100\right) = 2$
$\to {10}^{2} = 100$

$18 = {e}^{3 x}$
$\to {\log}_{e} \left(18\right) = 3 x$

${\log}_{e} \left(n\right) = \ln \left(n\right)$

enter $\to \ln \left(18\right)$ into a calculator:

$\to \ln \left(18\right) = 2.89037 . .$

$3 x = 2.8903717578961647$

divide this answer by $3$:

$x = 0.963 \left(3 s . f .\right)$