Answer
$x\approx0.0937$
Work Step by Step
Taking the logarithm of both sides, the given equation, $
7^x=1.2
,$ is equivalent to
\begin{align*}
\log7^x&=\log1.2
.\end{align*}
Using the properties of logarithms and of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
x\log7&=\log1.2
&(\log_b x^y=y\log_b x)
\\\\
\dfrac{x\cancel{\log7}}{\cancel{\log7}}&=\dfrac{\log1.2}{\log7}
\\\\
x&=\dfrac{\log1.2}{\log7}
\\\\
x&\approx0.0937
.\end{align*}
Hence, the solution to the equation $7^x=1.2$ is $x\approx0.0937$.
