Answer
$x\approx 3.07$
Work Step by Step
Take the natural log of both sides to obtain:
$\ln{(e^{\frac{3x}{4}})} = \ln{10}$
Use the rule $\log{(a^n)} = n\cdot\log{a}$ to obtain:
$\frac{3x}{4} \cdot \ln{e} = \ln{10}$
Use the rule $\ln{e} = 1$ to obtain:
$\frac{3x}{4} \cdot 1 = \ln{10}
\\\frac{3x}{4}= \ln{10}$
Multiply $\frac{4}{3}$ to both sides of the equation to obtain:
$\frac{3x}{4} \cdot \frac{4}{3}= \frac{4}{3} \cdot \ln{10}
\\x= \frac{4\ln{10}}{3}$
Use a calculator to obtain:
$x\approx 3.07$
