Answer
$x=\dfrac{\log3.8}{2\log3}\approx0.6076$
Work Step by Step
$3^{2x}=3.8$
Apply $\log$ to both sides of the equation:
$\log3^{2x}=\log3.8$
Take $2x$ down to multiply in front of its respective $\log$:
$2x\log3=\log3.8$
Solve for $x$:
$2x=\dfrac{\log3.8}{\log3}$
$x=\dfrac{\log3.8}{2\log3}\approx0.6076$
