Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 102

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\log _ { 6 } \sqrt [ 3 ] { \frac { \mathrm { x } ^ { 5 } \mathrm { y } } { 36 } }$

• A) \(\frac { 5 } { 3 } \log _ { 6 } x + \frac { 1 } { 3 } \log _ { 6 } y - \frac { 2 } { 3 }\)
• B) \(\frac { 1 } { 3 } \left( \log _ { 6 } x ^ { 5 } + \log _ { 6 } y - 2 \right)\)
• C) \(\frac { 1 } { 3 } \left( \log _ { 6 } x ^ { 5 } y - \log _ { 6 } 36 \right)\)
• D) \(\frac { 5 } { 3 } \log _ { 6 } x - \frac { 1 } { 3 } \log _ { 6 } y + \frac { 2 } { 3 }\)

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Definitions:

Replacement Chain Method

A decision analysis for evaluating the replacement of assets, considering the optimal time to replace each asset.

Time Horizons

The length of time over which an investment is intended to be held or a financial goal is expected to be achieved.

Present Values

The contemporary valuation of a forthcoming sum of money or cash flows, based on a given rate of return.

Cash Inflows

Money entering a business from various sources, including sales, financing, and investment income.