Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$2 \log _ { b } x - \log _ { b } y$
A) $\log _ { b } x ^ { 2 } \div \log _ { b } y$
B) $\log _ { b } \frac { x ^ { 2 } } { y }$
C) $\log _ { b } \left( x ^ { 2 } - y \right)$
D) $\log _ { b } \frac { 2 x } { y }$

Question

Quizplus · Accepted Answer

We can use the rule that $\log _ { b } x ^ n=n\log_bx$ to rewrite $2\log_bx$ as $\log_bx^2$. Then we can use the quotient rule for logarithms $\log_b\frac{x}{y}=\log_bx-\log_by$ to rewrite the expression as $\log _ { b } \frac { x ^ { 2 } } { y }$.

Rewrite as a Single Logarithm 2log⁡bx−log⁡by2 \log _ { b } x - \log _ { b } y2logb​x−logb​y

Rewrite as a Single Logarithm $2 \log _ { b } x - \log _ { b } y$