Use the Properties of Logarithms to Write the Expression as a Single

question 220

Multiple Choice

Use the properties of logarithms to write the expression as a single logarithm.
- $$\log _ { 5 } x + 3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$$

• A) \(\log _ { 5 } \left( \frac { x ^ { 2 } + 3 x } { x + 6 } \right)\)
• B) \(\log _ { 5 } \left( \frac { x ^ { 4 } } { x + 6 } \right)\)
• C) \(\log _ { 5 } \left( \frac { x ^ { 3 } } { x + 6 } \right)\)
• D) \(3 \log _ { 5 } \left( \frac { x ^ { 2 } } { x + 6 } \right)\)

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Definitions:

Sodium Hydroxide

A highly caustic metallic base and alkali salt, commonly known as lye or caustic soda, used in various industrial processes.

Carbonyl

A functional group in organic chemistry consisting of a carbon atom double-bonded to an oxygen atom.

Acetone

A volatile, flammable liquid used as a solvent and an antiseptic, known chemically as propanone.

Synthesize

To combine simpler substances chemically to form a more complex substance, often used in reference to the production of chemical compounds in a laboratory.