Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$

question 84

Multiple Choice

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
- $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$

• A) \(\frac { 1 } { 4 } \log _ { 3 } x - 1\)
• B) \(\log _ { 3 } x - \log _ { 3 } 4 - 1\)
• C) \(\frac { 1 } { 4 } \log _ { 3 } x - \frac { 1 } { 4 }\)
• D) \(\log _ { 3 } \sqrt [ 4 ] { x } - \log _ { 3 } \sqrt [ 4 ] { 3 }\)

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Definitions:

Income Equality

A measure or concept where everyone has the same income or very similar incomes, minimizing the gap between the wealthy and the poor.

Tax-Transfer Program

Government initiatives designed to redistribute income through the tax system, often aiming to reduce poverty.

Economic Equality

A state in which individuals or groups within a society have similar economic conditions, including access to resources, opportunities, and outcomes.

Income Inequality

The unequal distribution of income and wealth across individuals or groups within a society, often measured using tools like the Gini coefficient.