Express as the Logarithm of a Single Expression $3 \log _ { 3 } x + \frac { 1 } { 6 } \log _ { 3 } x - 2 \log _ { 3 } ( x + 1 )$

question 246

Multiple Choice

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
- $3 \log _ { 3 } x + \frac { 1 } { 6 } \log _ { 3 } x - 2 \log _ { 3 } ( x + 1 )$

• A) \(\log _ { 3 } \frac { \mathrm { x } ^ { 19 / 6 } } { 2 ( \mathrm { x } + 1 ) }\)
• B) \(\frac { 19 } { 6 } \log _ { 3 } \frac { x } { ( x + 1 ) ^ { 2 } }\)
• C) \(\log _ { 3 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }\)
• D) \(\log _ { 3 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)\)

---

Definitions:

Production Function

Function showing the highest output that a firm can produce for every specified combination of inputs.

Annual Output

The total production or quantity of goods and services produced by a company or economy in one year.

Economies of Scale

The cost advantage achieved by an increase in production, leading to a decrease in the average cost per unit through efficient allocation of resources and spreading of fixed costs.

Cost-output Elasticity

The ratio of the percentage change in cost relative to the percentage change in output, indicating how costs change with output levels.