Use Properties of Logarithms to Condense the Logarithmic Expression $5 \log _ { 6 } 5 + \frac { 1 } { 4 } \log _ { 6 } ( r - 2 ) - \frac { 1 } { 2 } \log _ { 6 } r$

question 148

Multiple Choice

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
- $5 \log _ { 6 } 5 + \frac { 1 } { 4 } \log _ { 6 } ( r - 2 ) - \frac { 1 } { 2 } \log _ { 6 } r$

• A) \(\log _ { 6 } \frac { 3125 r - 2 } { 8 r }\)
• B) \(\log _ { 6 } \frac { 3125 \sqrt [ 4 ] { \mathrm { r } - 2 } } { \sqrt { \mathrm { r } } }\)
• C) \(\log _ { 6 } \sqrt { \frac { 5 r - 10 } { 8 r } }\)
• D) \(\log _ { 6 } \left( \frac { 5 } { 8 } \sqrt { \frac { r - 2 } { r } } \right)\)

Recognize the relationship between tax rates and government revenue, including the Laffer curve implications.

Identify key characteristics of labor market responses to taxation.

Evaluate the effects of changes in tax rates on market equilibrium and welfare.

Distinguish between elastic and inelastic supply and demand contexts in relation to tax efficiency.

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Definitions:

General Anesthesia

General anesthesia is a medically induced coma and loss of protective reflexes resulting from the administration of one or more general anaesthetic agents, used during surgical procedures to ensure that patients are not awake or in pain.

Moderate Sedation

A type of anesthesia that depresses consciousness, allowing patients to tolerate unpleasant procedures while maintaining airway control and adequate cardiopulmonary function.

Regional Anesthesia

Anesthesia affecting a larger part of the body, achieved by blocking nerves in a specific area to prevent pain sensation.

Venous Return

The process of blood flowing back to the heart via the veins from the body's tissues, an essential component of circulatory health.