Solve the Logarithmic Equation $$\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$$

question 82

Multiple Choice

Solve the logarithmic equation. Give an exact solution.
- $$\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$$

• A) \(\left\{ \frac { 87 } { 26 } \right\}\)
• B) \(\{ 18 \}\)
• C) \(\left\{ \frac { 33 } { 8 } \right\}\)
• D) \(\left\{ \frac { 9 } { 26 } \right\}\)

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Definitions:

Aroused, Motivated State

A condition of being mentally and physically activated or energized towards achieving a specific goal.

Physiological Need

Physiological Need refers to basic physical requirements essential for human survival, such as food, water, and shelter, as defined in theories of motivation like Maslow's hierarchy of needs.

A Drive

A drive is a psychological state that motivates an organism to satisfy a need, often critical for survival, like hunger or thirst.

Sleepiness

A state of strong desire for sleep, or sleeping for unusually long periods (compare with fatigue).