Write the Logarithm as a Sum or Difference of Logarithms $$\log _ { 5 } \left[ \frac { 125 a ^ { 5 } \sqrt { 8 - b } } { c ( b + 7 ) ^ { 2 } } \right]$$

question 10

Multiple Choice

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
- $$\log _ { 5 } \left[ \frac { 125 a ^ { 5 } \sqrt { 8 - b } } { c ( b + 7 ) ^ { 2 } } \right]$$

• A) \(3 + 5 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } ( 8 - b ) - \log _ { 5 } c - 2 \log _ { 5 } ( b + 7 )\)
• B) \(15 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } 8 + \frac { 1 } { 2 } \log _ { 5 } b + \log _ { 5 } \mathrm { c } + 2 \log _ { 5 } b + 2 \log _ { 5 } 7\)
• C) \(3 + 5 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } 8 - \frac { 1 } { 2 } \log _ { 5 } b - \log _ { 5 } \mathrm { c } - 2 \log _ { 5 } b - 2 \log _ { 5 } 7\)
• D) \(15 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } ( 8 - b ) - \log _ { 5 } c - 2 \log _ { 5 } ( b + 7 )\)

---

Definitions:

Emotional Displacement

A defense mechanism where emotional reactions are transferred from one object or person to another that is less threatening.

Person-Centered Therapist

A professional who employs the principles of person-centered therapy, focusing on creating a non-judgmental and empathetic therapeutic environment to facilitate clients' self-discovery and personal growth.

Self-Actualization

The realization or fulfillment of one's talents and potentialities, considered as a drive or need present in everyone.

Anxiety and Defenses

Refers to how individuals experience nervousness or worry and the psychological mechanisms they employ to protect themselves from perceived threats.