Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$ ?
A) $\frac { 2 } { 7 } \log x - \frac { 4 } { 7 } \log y$
B) $\frac { 1 } { 14 } \log x + \frac { 1 } { 28 } \log y$
C) $\frac { 7 } { 2 } \log x + \frac { 7 } { 4 } \log y$
D) $14 \log x + 28 \log y$
E) $\frac { 2 } { 7 } \log x + \frac { 4 } { 7 } \log y$

Question

Quizplus · Accepted Answer

The expression can be expanded using the properties of logarithms as follows: $\log \sqrt[7]{\frac{x^2}{y^4}}$ can be rewritten as $\frac{1}{7}\log(\frac{x^2}{y^4})$, which further expands to $\frac{1}{7}(\log x^2 - \log y^4)$. Applying the power rule of logarithms, this becomes $\frac{2}{7}\log x - \frac{4}{7}\log y$.

Use the Properties of Logarithms to Expand the Expression as a Sum,difference,and/or