Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$\frac { 1 } { 3 } \left( \log _ { 4 } x + \log _ { 4 } y \right)$
A) $\sqrt [ 3 ] { \log _ { 4 } ( x y ) }$
B) $\log _ { 4 } \sqrt [ 3 ] { x + y }$
C) $\log _ { 4 } \sqrt [ 3 ] { x } + \log _ { 4 } \sqrt [ 3 ] { y }$
D) $\log _ { 4 } \sqrt [ 3 ] { x y }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to combine the logs inside the parentheses as $\log_4(xy)$, and the $\frac{1}{3}$ exponent outside becomes a cube root inside the log, resulting in $\log_4 \sqrt[3]{xy}$.

Use Properties of Logarithms to Condense the Logarithmic Expression 13(log⁡4x+log⁡4y)\frac { 1 } { 3 } \left( \log _ { 4 } x + \log _ { 4 } y \right)31​(log4​x+log4​y)

Use Properties of Logarithms to Condense the Logarithmic Expression $\frac { 1 } { 3 } \left( \log _ { 4 } x + \log _ { 4 } y \right)$