Answer
$2$
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 equation:
$\log_4{48}-\frac{1}{2}\log_4{9}\\
=\log_4{48}-\log_4{9^{1/2}}\\
=\log_4{48}-\log_4{\sqrt{9}}\\
=\log_4{48}-\log_4{3}$
Next, recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
We use this property to simplify our last expression:
$\log_4{48}-\log_4{3}\\
=\log_4{\frac{48}{3}}\\
=\log_4{16}$
Finally, we apply the power property once more to simplify:
$\log_4{16}\\
=\log_4{4^2}\\
=2\log_4{4}\\
=2\times 1\\
=2$
We also used the fact that $\log_{4}{4}=1$ (because $4^1=4$).
