Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { b } \left( y z ^ { 5 } \right)$
A) $5 \log _ { \mathrm { b } } \mathrm { y } + 5 \log _ { \mathrm { b } } \mathrm { z }$
B) $5 \log _ { \mathrm { b } } \mathrm { yz }$
C) $\log _ { \mathrm { b } } \mathrm { y } + 5 \log _ { \mathrm { b } } \mathrm { z }$
D) $\log _ { b } y + \log _ { b } 5 z$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the product property $\log_b(mn) = \log_b(m) + \log_b(n)$ and the power property $\log_b(m^n) = n \log_b(m)$, the expression $\log_b(yz^5)$ can be expanded to $\log_b(y) + 5\log_b(z)$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much