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

question 376

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
- $$\frac { 3 } { 4 } \log _ { a } \left( p ^ { 2 } q ^ { 8 } \right) - \frac { 1 } { 2 } \log _ { a } \left( p ^ { 5 } q ^ { 2 } \right)$$

• A) \(\log _ { a } \left( p ^ { 4 } q ^ { 7 } \right)\)
• B) \(\log _ { a } \left( \frac { 3 } { 4 } p ^ { 2 } q ^ { 8 } - \frac { 1 } { 2 } p ^ { 5 } q ^ { 2 } \right)\)
• C) \(\log _ { a } \left( \frac { 3 q ^ { 6 } } { 2 p ^ { 3 } } \right)\)
• D) \(\log _ { a } \left( \frac { q ^ { 5 } } { p } \right)\)

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Definitions:

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Weighted Average

A calculation that takes into account the varying degrees of importance of the numbers in a dataset, assigning weights to each number based on its significance.

Weighted Average

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FIFO

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