How do you solve e^(3x)=4?

Mar 27, 2018

$x = \ln \frac{4}{3} \approx 0.46$

Explanation:

Given: ${e}^{3 x} = 4$

Take natural logarithm of both sides.

$\ln \left({e}^{3 x}\right) = \ln 4$

$3 x = \ln 4$

Divide by $3$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \ln \frac{4}{3}$

$x = \ln \frac{4}{3}$