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

question 274

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
- $4 \log _ { a } m - \log _ { a } n$

• A) \(\log _ { a } \left( \frac { m ^ { 4 } } { n } \right)\)
• B) \(\log _ { a } \left( m ^ { 4 } - n \right)\)
• C) \(\log _ { a } \left( \frac { 4 m } { n } \right)\)
• D) \(\log _ { a } m ^ { 4 } \div \log _ { a } n\)

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Definitions:

Symbolize

To represent or stand for something else, often an abstract idea, by means of symbols.

Main Connective

The logical operator in a compound proposition that determines the proposition's overall truth value.

Truth Table

A table used in logic to determine the validity of a proposition by listing all possible scenarios and their corresponding truth values.

Truth-Value Assignment

The process of designating truth values (true or false) to the components (usually variables) of a logical expression or statement.