Write as the Sum And/or Difference of Logarithms $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$

question 460

Multiple Choice

Write as the sum and/or difference of logarithms. Express powers as factors.
- $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$

• A) \(6 \ln x + \frac { 1 } { 3 } \ln ( 1 + 3 x ) - 7 \ln ( x - 9 )\)
• B) \(\ln 6 + \ln x + \frac { 1 } { 9 } \ln ( 1 + 3 x ) - 7 \ln ( x - 9 )\)
• C) \(\ln 6 + \ln x - 9 \ln ( 1 + 3 x ) - 7 \ln ( x - 9 )\)
• D) \(\ln 6 + \ln x + \frac { 1 } { 9 } \ln ( 1 + 3 x ) - \ln 7 - \ln ( x - 9 )\)

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Definitions:

Real GDP

The calculation of a nation's economic productivity after accounting for variations in prices, either through inflation or deflation, illustrating the true amount of goods and services generated.

Malthus

Refers to Thomas Robert Malthus, an English economist and demographer best known for his theory that population growth will outpace agricultural production, leading to widespread famine and hardship.

Outward-Oriented Policies

Economic policies aimed at promoting international trade and investment, as opposed to inward-looking strategies focusing on domestic markets.

Productivity

The efficiency at which individuals, companies, or economies produce goods and services, usually measured as output per unit of input.