Answer
$x=\dfrac{1}{5}$
Work Step by Step
Using the properties of logarithms, the given expression, $
\ln5+\ln x=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
\ln(5\cdot x)=0
\\\\
\ln(5x)=0
\\\\
\log_e(5x)=0
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x$, then the solution to the equation, $
\log_e(5x)=0
,$ is
\begin{array}{l}\require{cancel}
5x=e^0
\\\\
5x=1
\\\\
x=\dfrac{1}{5}
.\end{array}
Upon checking, $
x=\dfrac{1}{5}
$ satisfies the original equation.
