Answer
$x=\dfrac{4}{3}\ln10\approx3.07$
Work Step by Step
$e^{3x/4}=10$
Apply $\ln$ to both sides of the equation:
$\ln e^{3x/4}=\ln10$
Take $\dfrac{3x}{4}$ down to multiply in front of its respective $\ln$:
$\dfrac{3x}{4}\ln e=\ln10$
Since $\ln e=1$, this equation becomes:
$\dfrac{3x}{4}=\ln10$
Solve for $x$:
$3x=4\ln10$
$x=\dfrac{4}{3}\ln10\approx3.07$