Answer
$x\approx43.301$
Work Step by Step
Using the properties of logarithms, the given equation, $
\ln e^{0.04x}=\sqrt{3}
$ is equivalent to
\begin{align*}\require{cancel}
0.04x\ln e&=\sqrt{3}
&(\text{use }\log_b x^y=y\log_b x)
\\
0.04x(1)&=\sqrt{3}
&(\text{use }\ln e=1)
\\
0.04x&=\sqrt{3}
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
\dfrac{\cancel{0.04}x}{\cancel{0.04}}&=\dfrac{\sqrt{3}}{0.04}
\\\\
x&=\dfrac{\sqrt{3}}{0.04}
\\\\
x&\approx43.301
.\end{align*}
Hence, the solution to the equation $
\ln e^{0.04x}=\sqrt{3}
$ is $
x\approx43.301
$.
