Use the Properties of Logarithms to Rewrite the Expression $\log _ { 2 } \left( \frac { x ^ { 9 } y ^ { 7 } } { 7 } \right)$

question 366

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log _ { 2 } \left( \frac { x ^ { 9 } y ^ { 7 } } { 7 } \right)$

• A) \(9 \log _ { 2 } x + 7 \log 2 y - \log _ { 2 } 7\)
• B) \(\left( 9 \log _ { 2 } x \right) \left( 7 \log _ { 2 } y \right) \div \log _ { 2 } 7\)
• C) \(\left( \log _ { 2 } x \right) ^ { 9 } + \left( \log _ { 2 } y \right) ^ { 7 } - \log _ { 2 } 7\)
• D) \(9 \log _ { 2 } x + 7 \log 2 y + \log _ { 2 } 7\)

---

Definitions:

Consequences

The outcomes or effects that stem from a particular action or decision, which can be intended or unintended and positive or negative.

Stability

The condition of an economy characterized by constant or predictable levels of growth, inflation, and employment.

Steady Rate

A constant or unchanging rate over a period of time, often used to describe economic growth, inflation, or other financial metrics.

Economic Growth

An increase in the production of goods and services in an economy over time, often measured by the rise in Gross Domestic Product (GDP).