Answer
$x = \dfrac{\ln{14}}{\ln{3}}\approx 2.402$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{3^x} = \ln{14}$
Use the rule $\ln{a^x} = x \cdot \ln{a}$ to obtain:
$x\cdot \ln{3} = \ln{14}$
Divide both sides of the equation by $\ln{3}$ to obtain:
$\dfrac{x\cdot \ln{3}}{\ln{3}}=\dfrac{\ln{14}}{\ln{3}}
\\x = \dfrac{\ln{14}}{\ln{3}}
\\x \approx 2.402$
