Combine into a Single Logarithm $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

question 2

Multiple Choice

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

• A) \(\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)
• B) \(\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }\)
• C) \(\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }\)
• D) \(\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)
• E) \(\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)

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Definitions:

Educated Guess

A hypothesis or assumption made based on knowledge and reasoning rather than random guessing.

Hypothesis

A preliminary hypothesis presented upon scant evidence, aimed at instigating further exploration.

Null Hypothesis

A statement used in statistical testing which suggests that there is no significant effect or difference.

Directional Research Hypothesis

A hypothesis that predicts not only that a relationship exists between variables but also the direction of that relationship.