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:

Contribution Margin

The amount of revenue remaining after deducting the variable costs, indicating the contribution towards the fixed costs and profits.

Annual Production

The total quantity of goods or output produced by a company in a year.

Variable Cost

A cost that varies in direct proportion to changes in the level of production or sales volume, such as materials and labor used in production.

Idle Capacity

Resources available for use that are not currently being utilized in the production process.