Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$5 \log _ { \mathrm { b } } \mathrm { y } + 8 \log _ { \mathrm { b } } \mathrm { z }$
A) $\log _ { b } y ^ { 5 } z$
B) $13 \log _ { b } y z$
C) $\log _ { b } ( y z ) ^ { 13 }$
D) $40 \log _ { \mathrm { b } } \mathrm { yz }$

Question

Quizplus · Accepted Answer

Using the power rule of logarithms, $a \log_b x = \log_b x^a$, the expression can be rewritten as $\log_b y^5 + \log_b z^8$. Then, applying the product rule, $\log_b x + \log_b y = \log_b (xy)$, the expression becomes $\log_b (y^5z^8)$.

Use Properties of Logarithms to Condense the Logarithmic Expression 5log⁡by+8log⁡bz5 \log _ { \mathrm { b } } \mathrm { y } + 8 \log _ { \mathrm { b } } \mathrm { z }5logb​y+8logb​z

Use Properties of Logarithms to Condense the Logarithmic Expression $5 \log _ { \mathrm { b } } \mathrm { y } + 8 \log _ { \mathrm { b } } \mathrm { z }$