Write the Expression $5 \ln ( x ) + 2 \ln ( x + 3 ) - 5 \ln ( x - 3 )$

question 20

Multiple Choice

Write the expression $5 \ln ( x ) + 2 \ln ( x + 3 ) - 5 \ln ( x - 3 )$ as the logarithm of a single quantity.

• A) \(\ln ( 2 x + 21 )\)
• B) \(\ln \left[ \frac { 10 \left( x ^ { 2 } + x \right) } { 5 ( x - 3 ) } \right]\)
• C) \(\ln \left( x ^ { 5 } ( x + 3 ) ^ { 2 } ( x - 3 ) ^ { 5 } \right)\)
• D) \(\ln \left[ \frac { x ^ { 5 } ( x + 3 ) ^ { 2 } } { ( x - 3 ) ^ { 5 } } \right]\)
• E) \(\ln \left[ \frac { x ^ { 5 } } { ( x + 3 ) ^ { 2 } ( x - 3 ) ^ { 5 } } \right]\)

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Definitions:

Closed-loop Control

A control system methodology where output is measured and continuously fed back into the system for real-time adjustments to achieve desired performance.

PLC Control

PLC (Programmable Logic Controller) control refers to the automation of machinery and processes using a specialized computer that executes instructions for logical operations, sequencing, timing, counting, and arithmetic to control machines and processes.

Desired Value

The target or setpoint value that a system or process aims to achieve or maintain.