Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.
A) $\log _ { 4 } \frac { ( 3 x ) ^ { 5 } } { y }$
B) $\log _ { 4 } \frac { 3 x } { 5 y }$
C) $\log _ { 4 } \sqrt [ 5 ] { \frac { 3 x } { y } }$
D) $\log _ { 4 } \frac { \sqrt [ 5 ] { 3 x } } { y }$
E) $\log _ { 4 } \sqrt [ 5 ] { 3 x } - \log _ { 4 } y$

Question

Quizplus · Accepted Answer

The expression can be condensed using the properties of logarithms: $\frac{1}{5}[\log_4 x + \log_4 3] = \log_4((3x)^{1/5})$. Subtracting $\log_4 y$ gives $\log_4 \frac{\sqrt[5]{3x}}{y}$.

Condense the Expression 15[log⁡4x+log⁡43]−[log⁡4y]\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]51​[log4​x+log4​3]−[log4​y]

Condense the Expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]$