Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 146

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\log \left[ \frac { 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } } { 10 ( x + 3 ) ^ { 2 } } \right]$

• A) \(\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 - 2 \log ( x + 3 )\)
• B) \(\log 4 + \log x ^ { 3 } + \log ( 3 - x ) ^ { 1 / 4 } - \log 10 - \log ( x + 3 ) ^ { 2 }\)
• C) \(\log \left( 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } \right) - \log \left( 10 ( x + 3 ) ^ { 2 } \right)\)
• D) \(\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 + 2 \log ( x + 3 )\)

---

Definitions:

Self-Esteem

The confidence and sense of respect one has for themselves; self-worth.

Supportive Leadership

A leadership style that focuses on building trust, respect, and empathy with team members while encouraging their development and well-being.

Planning

The process of outlining the steps necessary to achieve a desired outcome or goal, involving setting objectives, determining actions, and allocating resources.

Key Components

Essential parts, elements, or factors that are necessary for the functioning or effectiveness of a system, process, or concept.