Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$$( \log b x - \log b y ) + 6 \log b z$$
A) $\log _ { b } \frac { x z ^ { 6 } } { y }$
B) $\log _ { b } \frac { 6 x z } { y }$
C) $\log _ { b } x z ^ { 6 } y$
D) $\log _ { a } \frac { x } { z ^ { 6 } y }$

Question

Quizplus · Accepted Answer

We can use the rules of logarithms to combine the terms:

$$( \log b x - \log b y ) + 6 \log b z = \log b \frac{x}{y} + \log b z^6$$
Now we can use the rule that $\log a + \log b = \log(ab)$ to combine the logs:

$$\log b \frac{x}{y} + \log b z^6 = \log b \left(\frac{xz^6}{y}\right)$$
Therefore, the answer is $\boxed{\textbf{(A)}}$.

Rewrite as a Single Logarithm (log⁡bx−log⁡by)+6log⁡bz( \log b x - \log b y ) + 6 \log b z(logbx−logby)+6logbz

Rewrite as a Single Logarithm $( \log b x - \log b y ) + 6 \log b z$