Answer
$\log_4(x^6\cdot\sqrt [4]x)$
Work Step by Step
We can write the expression as a single logarithm using the rule:
$\log_b(m)+\log_b(n)=\log_b(m\cdot n)$
So,
$3\log_4x^2+\frac{1}{2}\log_4\sqrt x=$
$\log_4(x^2)^3+\log_4(\sqrt x)^{\frac{1}{2}}=$
$\log_4x^6+\log_4\sqrt [4]x=$
$\log_4(x^6\cdot\sqrt [4]x)$
