Write as the Sum or Difference of Logarithms and Fully $\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)$

question 93

Multiple Choice

Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable
represents a positive real number.
- $\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)$

• A) \(3 - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)\)
• B) \(3 + \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)\)
• C) \(3 - \log \left( \sqrt { x ^ { 2 } + 25 } \right)\)
• D) \(3 - \log ( x + 5 )\)

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Definitions:

Availability Heuristic

A mental shortcut that relies on immediate examples that come to mind when evaluating a specific topic, concept, method, or decision.

Fundamental Attribution Error

The tendency to overestimate the influence of personality and underestimate the impact of situational factors on other people's behavior.

False Consensus Effect

The tendency for people to overestimate the extent to which their beliefs, opinions, preferences, values, and habits are normal and typical of those of others.

Counterfactual Thinking

The human tendency to create possible alternatives to life events that have already occurred, something akin to imagining "what might have been."