Answer
$x = \dfrac{\log{3.8}}{2\log{3}}x \approx 0.6076$
Work Step by Step
Take the common logarithm of both sides to have:
$\log{3^{2x}}=\log{3.8}$
Apply the power property of logarithms to have:
$2x(\log{3}) = \log{3.8}$
Divide $2\log{3}$ to both sides to have:
$\\x = \dfrac{\log{3.8}}{2\log{3}}
\\x \approx 0.6076$
