Answer
$x=0$
Work Step by Step
Using the properties of equality, the given equation, $
4+5e^{-x}=9
,$ is equivalent to
\begin{array}{l}\require{cancel}
5e^{-x}=9-4
\\\\
5e^{-x}=5
\\\\
e^{-x}=\dfrac{5}{5}
\\\\
e^{-x}=1
.\end{array}
Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $
e^{-x}=1
,$ is
\begin{array}{l}\require{cancel}
\ln e^{-x}=\ln 1
\\\\
-x(\ln e)=\ln 1
\\\\
-x(1)=\ln 1
\\\\
-x=\ln 1
\\\\
x=-\ln 1
\\\\
x=0
.\end{array}
