Answer
$\log_3{\sqrt[4]{2x}}$
Work Step by Step
Recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
We apply this property to the given expression to obtain:
$\frac{1}{4}\log_3{2}+\frac{1}{4}\log_3{x}=\log_3{2^{\frac{1}{4}}}+\log_3{x^{\frac{1}{4}}}$
Next, recall the product property of logarithms (pg. 462):
$\log_b{mn}=\log_b{m}+\log_b{n}$
Applying this property, we get:
$\log_3{2^{\frac{1}{4}}}+\log_3{x^{\frac{1}{4}}}\\
=\log_3{2^{1/4}x^{1/4}}\\
=\log_3{(2x)^{1/4}}\\
=\log_3{\sqrt[4]{2x}}$
