Express as a Single Logarithm $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

question 225

Multiple Choice

Express as a single logarithm.
- $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

• A) \(\log _ { a } 2 ( x + 1 )\)
• B) \(\log _ { a } ( 2 x + 1 ) + 2\)
• C) \(\log _ { a } ( 2 x + 3 )\)
• D) \(\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }\)

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Definitions:

Unwarranted Assumptions

Assumptions made without sufficient evidence, often leading to flawed reasoning or conclusions.

Modus Ponens

a logical argument form and principle of inference where if a conditional statement ("if P, then Q") is accepted, and the antecedent (P) holds, then the consequent (Q) can be concluded.

Modus Tollens

A form of logical argument where the consequent is negated, leading to the negation of the antecedent.

Antecedent

A thing or event that exists or comes before another in time or logically precedes it.