Write as the Sum And/or Difference of Logarithms $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

question 259

Multiple Choice

Write as the sum and/or difference of logarithms. Express powers as factors.
- $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

• A) \(6 \log _ { 3 } y - 2 \log _ { 3 } x\)
• B) \(2 \log _ { 3 } x + 6 \log _ { 3 } y\)
• C) \(\frac { 1 } { 3 } \log _ { 3 } \left( \frac { \mathrm { x } } { \mathrm { y } } \right)\)
• D) \(2 \log _ { 3 } x - 6 \log _ { 3 } y\)

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Definitions:

Tiebout Hypothesis

A theory suggesting that people will migrate to local jurisdictions that best satisfy their preferences for public goods and services, reflecting a form of market efficiency in local government.

Public Good

A good that is non-excludable and non-rivalrous, meaning it can be used by many people simultaneously without depletion.

Free-rider Problem

A situation in which some individuals consume more than their fair share of a public resource, or shoulder less of the cost of its production, benefiting from goods or services without paying for them.

Nonexcludable Problem

An issue characteristic of public goods, where it is not possible to prevent individuals who do not pay from consuming a good or service.