Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 38

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible.
- $\log_ 5 \frac { d ^ { 4 } } { ( c - 5 ) ^ { 2 } }$

• A) \(4 \log _ { 5 } d - 2 \log _ { 5 } ( c - 5 )\)
• B) \(\frac { 4 \log _ { 5 } d } { 2 \log _ { 5 } ( c - 5 ) }\)
• C) \(\frac { 4 \log _ { 5 } \mathrm {~d} } { 2 \log _ { 5 } c~ - ~2 \log _ { 5 } 5 }\)
• D) \(2 \left( \log _ { 5 } d - \log_ 5 ( c - 5 ) \right)\)

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Definitions:

Social Structure

The organized pattern of relationships and social institutions that together compose society, including roles, classes, and social hierarchies.

Republican Society

A social order that emphasizes the welfare of the community and operates on principles of democracy and the rule of law, often in contrast to a monarchy or dictatorship.

Common Good

The benefit or interests of all participants in a society, considered as a guiding principle for governance and public policy.

Standard Deviation

A measure of the dispersion or variability of a set of values around the mean.