Answer
$\log_4{\left(\dfrac{m^x\sqrt[y]n}{p}\right)}$
Work Step by Step
Recall the basic properties of logarithms (pg. 462):
Product Property:
$\log_b{mn}=\log_b{m}+\log_b{n}$
Quotient Property:
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
Power Property:
$\log_b{m^n}=n\log_b{m}$
First, apply the power property to obtain:
:
$\log_4{m^x}+\log_4{n^{\frac{1}{y}}}-\log_4{p}$
Next, apply the product property to obtain:
$\log_4{(m^x\cdot n^{\frac{1}{y}})}-\log_4{p}$
Finally, apply the quotient property:
$=\log_4{\left(\dfrac{m^x\cdot n^{1/y}}{p}\right)}$
$=\log_4{\left(\dfrac{m^x\cdot \sqrt[y]n}{p}\right)}$
