Answer
$x\approx2.82$
Work Step by Step
Taking the logarithm of both sides, the value of $x$ in the expression $
10^{0.3x}=7
$ is,
\begin{array}{l}
\log10^{0.3x}=\log7\\
0.3x(\log10)=\log7\\
0.3x(1)=\log7\\
0.3x=\log7\\
3x=10\log7\\
x=\dfrac{10\log7}{3}\\
x\approx2.82
.\end{array}
