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

question 265

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
- $$\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z$$

• A) \(\log _ { a } \left( \frac { x z ^ { 5 } } { y } \right)\)
• B) \(\log _ { a } \left( \frac { 5 x z } { y } \right)\)
• C) \(\log _ { a } \left( x + z ^ { 5 } - y \right)\)
• D) \(\log _ { a } \left( \frac { x } { z ^ { 5 } y } \right)\)

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Definitions:

Cyclical Unemployment

Unemployment caused by the downturns of the economic cycle, such as recessions.

Natural Rate of Unemployment

The level of unemployment consistent with a stable rate of inflation, caused by the supply and demand for labor adjusting to various market factors.

Actual Rate of Unemployment

The proportion of the labor force that is jobless and actively looking for employment at any given time.

Labor Force

The total number of people available to work, including both the employed and the unemployed individuals actively seeking employment.