Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Expand the logarithm
![Certainly! Here's the transcription for an educational website:
---
### Logarithmic Expression
**Problem 36**:
Evaluate the logarithmic expression:
\[
\log_7 \left( \frac{x}{y^5} \right)^6
\]
**Explanation**:
This expression involves a logarithm with base 7. The expression inside the logarithm is a fraction raised to a power. Specifically, the numerator is \( x \) and the denominator is \( y \) raised to the fifth power. The entire fraction is then raised to the sixth power.
To simplify:
- Use the logarithmic power rule: \(\log_b (m^n) = n \cdot \log_b m\).
Apply this rule to rewrite the expression.
---
Feel free to explain the mathematical steps and properties used to further simplify the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccd31d51-5547-432f-9e2c-ede411255c83%2Fb9158eb2-e78c-4432-ba99-9153fbfad45d%2Fcng7v9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here's the transcription for an educational website:
---
### Logarithmic Expression
**Problem 36**:
Evaluate the logarithmic expression:
\[
\log_7 \left( \frac{x}{y^5} \right)^6
\]
**Explanation**:
This expression involves a logarithm with base 7. The expression inside the logarithm is a fraction raised to a power. Specifically, the numerator is \( x \) and the denominator is \( y \) raised to the fifth power. The entire fraction is then raised to the sixth power.
To simplify:
- Use the logarithmic power rule: \(\log_b (m^n) = n \cdot \log_b m\).
Apply this rule to rewrite the expression.
---
Feel free to explain the mathematical steps and properties used to further simplify the problem.
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