Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 32

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
- $\log _ { 5 } \frac { 125 } { \sqrt { x - 1 } }$

• A) \(3 - \log _ { 5 } \sqrt { x - 1 }\)
• B) \(3 \log _ { 5 } 5 - \frac { 1 } { 2 } \log _ { 5 } ( x - 1 )\)
• C) \(\log _ { 5 } 125 - \log _ { 5 } \sqrt { x - 1 }\)
• D) \(3 - \frac { 1 } { 2 } \log _ { 5 } ( x - 1 )\)

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Definitions:

Causal Variable

A causal variable is a factor that brings about change in another variable or set of variables, establishing a cause-and-effect relationship.

Correlational Method

A research technique that establishes the relationship (not necessarily causal) between two variables, traditionally denoted x and y, by measuring both variables in a sample of participants.

Random Assignment

Random assignment is a method used in experiments to randomly allocate participants to different groups, ensuring that each group is comparable at the start of the experiment.

Measurement Biases

Involves errors or inaccuracies in data collection, interpretation, or analysis due to systemic factors.