Write the Expression as a Single Logarithm with Coefficient 1 $a \neq 1 \text { and } b \neq 1$

question 378

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
- $3 \log _ { a } x - 9 \log _ { a } z ^ { 2 }$

• A) \(\frac { \log _ { a } x ^ { 3 } } { \log _ { a } z ^ { 18 } }\)
• B) \(\log _ { a } \left( \frac { x ^ { 3 } } { z ^ { 11 } } \right)\)
• C) \(\log _ { a } \left( \frac { x ^ { 3 } } { z ^ { 18 } } \right)\)
• D) \(\log _ { a } \left( \frac { 3 x } { 9 z ^ { 2 } } \right)\)

---

Definitions:

Industrialized Countries

Nations with significant levels of industrial activity, characterized by a high GDP and a well-developed infrastructure.

Capricious Universe

A concept suggesting the universe operates in a manner that is unpredictable and subject to sudden and unaccountable changes.

Productive Efforts

Refers to activities or endeavors that lead to the creation of goods, services, or value, contributing to economic productivity.