Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 8 } \sqrt [ 3 ] { y _ { \sqrt { 8 } } }$

question 152

Multiple Choice

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
- $\log _ { 8 } \sqrt [ 3 ] { y _ { \sqrt { 8 } } }$

• A) \(\frac { 1 } { 3 } \log _ { 8 } y + \frac { 1 } { 2 }\)
• B) \(\frac { 1 } { 3 } \log _ { 8 } y - \frac { 1 } { 6 }\)
• C) \(\frac { 1 } { 3 } \log _ { 8 } y - \frac { 1 } { 2 }\)
• D) \(\frac { 1 } { 3 } \log _ { 8 } y + \frac { 1 } { 6 }\)

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Definitions:

Producer Surplus

Producer surplus is the difference between what producers are willing to sell a good for and the actual price they receive.

Total Surplus

The sum of consumer surplus and producer surplus in a market, representing the total benefits to society from the trading of goods or services.

Equilibrium Price

The market price at which the quantity of a good demanded equals the quantity supplied, leading to a stable market condition.

Equilibrium Quantity

The quantity of goods or services supplied is equal to the quantity demanded at the market equilibrium price.