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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Definitions:

Antarctica

The Earth's southernmost continent, containing the geographic South Pole, noted for its vast ice sheets and extreme cold temperatures.

Mesozoic

The geological era that lasted from about 252 to 66 million years ago, including the Triassic, Jurassic, and Cretaceous periods, known for the dominance and eventual extinction of dinosaurs.

Gondwana

An ancient supercontinent that included present-day Africa, South America, Antarctica, India, and Australia, existing from the late Neoproterozoic until its break-up in the Jurassic period.

Southern Hemisphere

The half of Earth that lies south of the Equator, encompassing continents like Australia, Antarctica, and parts of Africa, South America, and Asia.