Use the Properties of Logarithms to Expand the Expression as a Sum

question 39

Multiple Choice

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$$\ln \frac { x } { \sqrt [ 3 ] { x ^ { 5 } - 2 } }$$

• A) \(\ln x + \frac { 5 } { 3 } \ln ( x - 2 )\)
• B) \(- \frac { 2 } { 3 } \ln x + \ln ( - 2 )\)
• C) \(- \frac { 2 } { 3 } \ln x - \ln ( - 2 )\)
• D) \(\ln x - \frac { 5 } { 3 } \ln ( x - 2 )\)
• E) \(\quad \ln x - \frac { 1 } { 3 } \ln \left( x ^ { 5 } - 2 \right)\)

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Definitions:

Flexibly Receptive

Openness to change and new ideas, while being able to adapt and respond positively to different circumstances and challenges.

Personality Characteristics

The distinct traits or qualities that define an individual’s patterns of thought, feeling, and behavior.

Success

The achievement of set goals or objectives, often measured by factors such as performance, attainment of desired outcomes, or recognition.

Big Five

A theory describing human personality as composed of five broad traits: openness, conscientiousness, extraversion, agreeableness, and neuroticism.