Solve the Exponential Equation $$4 ^ { x + 6 } = 7$$

question 178

Multiple Choice

Solve the exponential equation. Express the solution set in terms of natural logarithms.
- $$4 ^ { x + 6 } = 7$$

• A) \(\left\{ \frac { \ln 4 } { \ln 7 } + \ln 6 \right\}\)
• B) \(\{ \ln 7 - \ln 4 - \ln 6 \}\)
• C) \(\left\{ \frac { \ln 7 } { \ln 4 } - 6 \right\}\)
• D) \(\left\{ \frac { \ln 4 } { \ln 7 } + 6 \right\}\)

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Definitions:

Total Individual Benefit

The total value or satisfaction that an individual derives from consuming a particular quantity of goods or services.

Marginal Benefit

The supplementary enjoyment or advantage gained by consuming another unit of a good or service.

Marginal Social Benefit

The additional benefit received by society as a whole from the production or consumption of one more unit of a good.

Marginal Social Benefit

The additional gain to society as a whole from an additional unit of a good or service, considering both private benefits and externalities.