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

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to combine the expression 7(log x - log y) into a single logarithm as $\log \left( \frac { x } { y } \right) ^ { 7 }$. This is because subtracting two logarithms is equivalent to the logarithm of the division of their arguments, and multiplying a logarithm by a number is equivalent to raising its argument to the power of that number.

Condense the Expression 7(log X - Log Y) to the Logarithm