Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 85

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\log _ { a } \left( \frac { x ^ { 4 } \sqrt [ 3 ] { x + 5 } } { ( x - 2 ) ^ { 2 } } \right)$

• A) \(4 \log _ { a } x + \frac { 1 } { 3 } \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )\)
• B) \(4 \log _ { a } x - 3 \log _ { a } ( x + 5 ) - 2 \log _ { a } ( x - 2 )\)
• C) \(\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { - 3 } - \log _ { a } ( x - 2 ) ^ { 2 }\)
• D) \(\log _ { a } x ^ { 4 } + \log _ { a } ( x + 5 ) ^ { 1 / 3 } - \log _ { a } ( x - 2 ) ^ { 2 }\)

---

Definitions:

Pretax Financial Income

The amount of income that a company has earned before any taxes have been deducted, as reported on the income statement.

Comprehensive

Including or dealing with all or nearly all elements or aspects of something.

Partial

Pertaining to something that is not whole or complete, often used in financial contexts to describe payments, completion of tasks, or fulfillment of obligations that are not entirely settled.