Answer
$x\approx0.631$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
9^x=4
,$ take the logarithm of both sides. Use the properties of logarithms and of equality to isolate the variable. Approximate the answer with $3$ decimal places.
$\bf{\text{Solution Details:}}$
Taking the logarithm of both sides results to
\begin{array}{l}\require{cancel}
\log9^x=\log4
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
x\log9=\log4
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x=\dfrac{\log4}{\log9}
\\\\
x\approx0.631
.\end{array}