Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 56

Multiple Choice

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

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

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Definitions:

ΣX / N

The formula for calculating the mean of a set of data, where ΣX is the sum of all data points and N is the number of data points.

Arithmetic Average

Another term for the mean, calculated as the sum of all values divided by the number of values.

Frequency Value

The count of how many times a specific data point or value appears within a dataset.

Central Tendency

A measure that represents the center or typical value of a dataset, which includes the mean, median, and mode.