Condense the expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$ to the logarithm of a single term.
A) $\log _ { 6 } \frac { ( 7 x ) ^ { 3 } } { y }$
B) $\log _ { 6 } \frac { \sqrt [ 3 ] { 7 x } } { y }$
C) $\log _ { 6 } \sqrt [ 3 ] { \frac { 7 x } { y } }$
D) $\log _ { 6 } \sqrt [ 3 ] { 7 x } - \log _ { 6 } y$
E) $\log _ { 6 } \frac { 7 x } { 3 y }$

Question

Quizplus · Accepted Answer

The expression can be condensed using the properties of logarithms: $\frac{1}{3}[\log_{6}x + \log_{6}7] = \log_{6}\sqrt[3]{7x}$. Subtracting $\log_{6}y$ gives $\log_{6}\frac{\sqrt[3]{7x}}{y}$.

Condense the Expression 13[log⁡6x+log⁡67]−[log⁡6y]\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]31​[log6​x+log6​7]−[log6​y]

Condense the Expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$