Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$\frac { 2 } { 7 } \log _ { a } x + \frac { 1 } { 5 } \log _ { a } y$
A) $\frac { 2 } { 35 } \log _ { a } x y$
B) $\log _ { a } \left( x ^ { 2 / 7 } y ^ { 1 / 5 } \right)$
C) $\log _ { a } \left( y ^ { 2 / 35 } \right)$
D) $\log _ { a } \left( x y ^ { 2 / 35 } \right)$

Question

Quizplus · Accepted Answer

Using the power rule of logarithms, $\frac{2}{7}\log_a x$ becomes $\log_a x^{2/7}$ and $\frac{1}{5}\log_a y$ becomes $\log_a y^{1/5}$. Then, applying the product rule, these can be combined into a single logarithm as $\log_a (x^{2/7}y^{1/5})$.

Use the Product, Quotient, and Power Rules of Logarithms to Rewrite