Express the Following as a Single Logarithm $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

question 67

Multiple Choice

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

• A) \(\log b \left( \frac { x ^ { 3 } \sqrt { x - 2 } } { ( 3 x + 8 ) ^ { 7 } } \right)\)
• B) \(\log b \left( \frac { ( x - 2 ) ^ { 7 } \sqrt { x } } { ( 3 x + 8 ) ^ { 3 } } \right)\)
• C) \(\log b \left( \frac { x ^ { 7 } } { \sqrt { x - 2 } ( 3 x + 8 ) ^ { 3 } } \right)\)
• D) \(\log b \left( \frac { x ^ { 7 } } { \sqrt { 3 x + 8 } ( x - 2 ) ^ { 3 } } \right)\)

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A mental shortcut that relies on immediate examples that come to mind when evaluating a specific topic, concept, method, or decision.

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A cognitive bias where an individual's subjective confidence in their own abilities is greater than their objective accuracy.

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