Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$\log _ { 5 } x - 8 \log _ { 5 } y - 9 \log _ { 5 } z$$
A) $\log _ { 5 } \frac { x } { y ^ { 8 } z ^ { 9 } }$
B) $\log _ { 5 } \left( x - y ^ { 8 } - z ^ { 9 } \right)$
C) $\log _ { 5 } \frac { x } { 72 y z }$
D) $\log _ { 5 } ( x - 8 y - 9 z )$

Question

Quizplus · Accepted Answer

The expression can be simplified using the logarithm rules: $\log_b a - \log_b c = \log_b \frac{a}{c}$ and $\log_b a^n = n \log_b a$. Applying these rules, the expression simplifies to $\log_5 \frac{x}{y^8z^9}$.

Write the Logarithmic Expression as a Single Logarithm with Coefficient log⁡5x−8log⁡5y−9log⁡5z\log _ { 5 } x - 8 \log _ { 5 } y - 9 \log _ { 5 } zlog5​x−8log5​y−9log5​z

Write the Logarithmic Expression as a Single Logarithm with Coefficient $\log _ { 5 } x - 8 \log _ { 5 } y - 9 \log _ { 5 } z$