Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 29

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 4 } } \right)$

• A) \(\log _ { \mathrm { b } } \mathrm { x } + 5 \log _ { \mathrm { b } } \mathrm { y } - 4 \log _ { \mathrm { b } } z\)
• B) \(\log _ { b } x + \log _ { b } y ^ { 5 } - \log _ { b } z ^ { 4 }\)
• C) \(\log _ { b } x + 5 \log _ { b } y + 4 \log _ { b } z\)
• D) \(\log _ { \mathrm { b } } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 5 } + \log _ { \mathrm { b } } \mathrm { z } ^ { 4 }\)

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Definitions:

Crowding-in

An economic phenomenon where increased government spending leads to higher private sector investment.

Crowding-out

A situation where increased public sector spending reduces the amount of available funds for private sector investments.

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The total amount of money that a country's government has borrowed, typically as a result of deficit spending, and yet to repay.

Social Security Tax Surplus

The excess of revenues collected for Social Security over the expenditures on the program.