Answer
$x\approx1.134$
Work Step by Step
Using the properties of equality, the given equation, $
29=3e^{2x}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{29}{3}=e^{2x}
.\end{array}
Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $
\dfrac{29}{3}=e^{2x}
,$ is
\begin{array}{l}\require{cancel}
\ln\dfrac{29}{3}=\ln e^{2x}
\\\\
\ln\dfrac{29}{3}=2x(\ln e)
\\\\
\ln\dfrac{29}{3}=2x(1)
\\\\
\ln\dfrac{29}{3}=2x
\\\\
\dfrac{\ln\dfrac{29}{3}}{2}=x
\\\\
x\approx1.134
.\end{array}
