Express as a single logarithm.
-$8 \log _ { \mathrm { b } } 8 + 9 \log _ { \mathrm { b } } 3$
A) $\log _ { \mathrm { b } } 88 \cdot \log _ { \mathrm { b } } 3 ^ { 9 }$
B) $\log _ { b } 883 ^ { 9 }$
C) $\log _ { \mathrm { b } } ( 64 + 27 )$
D) $\log _ { \mathrm { b } } \frac { 88 } { 3 ^ { 9 } }$

Question

Quizplus · Accepted Answer

Using the logarithm power rule, $m \log_b x = \log_b x^m$, the expression becomes $\log_b 8^8 + \log_b 3^9$. Then, applying the product rule for logarithms, $\log_b x + \log_b y = \log_b (xy)$, the expression simplifies to $\log_b (8^8 \cdot 3^9)$, which is equivalent to $\log_b 883^9$.

Express as a Single Logarithm 8log⁡b8+9log⁡b38 \log _ { \mathrm { b } } 8 + 9 \log _ { \mathrm { b } } 38logb​8+9logb​3

Express as a Single Logarithm $8 \log _ { \mathrm { b } } 8 + 9 \log _ { \mathrm { b } } 3$