Answer
$\log_4 (x^{25/4})$
or
$\frac{25}{4}\log_4 (x)$
Work Step by Step
Use rule $\log_a (x^n) =n \log_a (x)$ to obtain:
$3 \log_4 (x^2) +\dfrac{1}{2} \log_4 x^{1/2}=\log_4 (x^{6}) +\log_4 x^{\frac{1}{4}}$
Now, use rule $\log_a{(mn)}=\log_a{m} + \log_a{n}$ to obtain:
$\log_4 (x^6) +\log_4 \sqrt[4] x=\log_4 (x^{6+\frac{1}{4}}) \\=\log_4 (x^{25/4})$
We can apply the first rule again to take out the exponent:
$\frac{25}{4}\log_4 (x)$
