Use the Change of Base Formula and the Properties of Logarithms

question 120

Multiple Choice

Use the change of base formula and the properties of logarithms to rewrite the expression as a single logarithm in the
indicated base.
- $\log 81 x ^ { 12 } + \log 27 y ^ { 9 } - \log _ { 9 } w ^ { 6 }$ , base 3

• A) \(\log _ { 3 } \frac { x ^ { 12 } y ^ { 9 } } { z ^ { 6 } }\)
• B) \(\log _ { 3 } \frac { x ^ { 3 } y ^ { 3 } } { z ^ { 3 } }\)
• C) \(\log _ { 3 } \left( x ^ { 3 } + y ^ { 3 } - z ^ { 3 } \right)\)
• D) \(\log _ { 3 } x ^ { 3 } y ^ { 3 } z ^ { 3 }\)

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Definitions:

Periods

Intervals of time into which financial or operational activities are divided for reporting, planning, or analysis purposes.

Future Value

The value of an investment or sum of money at a specified date in the future, taking into account interest or capital gains.

Ordinary Annuity

A series of equal payments made at fixed intervals over a specified period.

Ordinary Annuities

A sequence of identical payments distributed at the conclusion of successive intervals during a predetermined duration.