Use the Properties of Logarithms to Rewrite the Expression $\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$

question 336

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$
$\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7$

• A) \(\left( \log _ { 8 } 4 \right) \left( \frac { 1 } { 2 } \log _ { 8 } 7 \right) - \log _ { 8 } 8\)
• B) \(\frac { \log 88 } { 2 }\)
• C) \(\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7 - \log _ { 8 } 8\)
• D) \(\log _ { 8 } 4 + \sqrt { \log _ { 8 } 7 } - \log 88\)

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Definitions:

Positive Externalities

Benefits experienced by third parties or society at large as a result of an economic activity, without the third party incurring any cost.

Public Goods

Goods that are non-excludable and non-rivalrous, meaning no one can be prevented from using them and one person's use does not reduce availability to others.

Consumer Surplus

The gap between what consumers are prepared and can afford to pay for a product or service, and what they end up paying in reality.

Producer Surplus

The difference between the amount producers are willing to accept for a good versus what they actually receive.