Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent
positive real numbers.
-$\log _ { x } ( 3 y z )$
A) $\log _ { x } ( 3 + y + z )$
B) $\log _ { x } 3 + \log _ { x } y + \log _ { x } z$
C) $\left( \log _ { x } 3 \right) \left( \log _ { x } y \right) \left( \log _ { x } z \right)$
D) $\log _ { 3 } y + \log _ { 3 } z$

Question

Quizplus · Accepted Answer

Using the product rule, we can rewrite the expression as:
\begin{align*}
\log_x(3yz) &= \log_x(3) + \log_x(y) + \log_x(z) \
&= \log_x 3 + \log_x y + \log_x z
\end{align*} 
Therefore, the answer is B.

Rewrite as the Sum of Two or More Logarithms Using log⁡x(3yz)\log _ { x } ( 3 y z )logx​(3yz)

Rewrite as the Sum of Two or More Logarithms Using $\log _ { x } ( 3 y z )$