Write the Expression as a Single Logarithm with Coefficient 1 $a \neq 1 \text { and } b \neq 1$

question 346

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
- $3 \log _ { 4 } ( 4 x - 2 ) + 6 \log _ { 4 } ( 2 x + 7 )$

• A) \(\log _ { 4 } \left( ( 4 x - 2 ) ^ { 3 } + ( 2 x + 7 ) ^ { 6 } \right)\)
• B) \(\log _ { 4 } ( 4 x - 2 ) ^ { 3 } ( 2 x + 7 ) ^ { 6 }\)
• C) \(18 \log _ { 4 } ( 4 x - 2 ) ( 2 x + 7 )\)
• D) \(\log _ { 4 } \frac { ( 4 x - 2 ) ^ { 3 } } { ( 2 x + 7 ) ^ { 6 } }\)

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Definitions:

Meters Per Second

A measurement of speed indicating how many meters are traveled in one second.

Action Potential

A rapid rise and subsequent fall in voltage or membrane potential across a cellular membrane with a characteristic pattern, crucial for nerve signal transmission.

Refractory Periods

Refractory periods are times following an action potential during which a neuron is less responsive to stimuli, ensuring the unidirectional flow of the signal.

Synaptic Knob

The end part of an axon that makes a synaptic contact with another neuron, responsible for the release of neurotransmitters.