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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Question
Use properties of logarithms to expand the logarithmic expression as much as possible (and show how to do the problem/show the work)
![The expression presented is:
\[ \log_4 \sqrt[7]{\frac{x^4y}{16}} \]
This is a logarithmic function with base 4, applied to the seventh root of the fraction \(\frac{x^4y}{16}\).
- The **numerator** of the fraction is \(x^4y\), which indicates that \(x\) is raised to the fourth power and multiplied by \(y\).
- The **denominator** is 16.
- The radical symbol indicates a seventh root, applied to the entire fraction \(\frac{x^4y}{16}\).
In an educational context, this expression showcases the use of logarithmic functions in conjunction with roots and fractions, demonstrating complex mathematical operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcea6d79-c0c2-49cd-aa31-c3eca199518f%2F06418f55-60f8-4964-8fd3-5744414157bf%2Frjdus4j_processed.png&w=3840&q=75)
Transcribed Image Text:The expression presented is:
\[ \log_4 \sqrt[7]{\frac{x^4y}{16}} \]
This is a logarithmic function with base 4, applied to the seventh root of the fraction \(\frac{x^4y}{16}\).
- The **numerator** of the fraction is \(x^4y\), which indicates that \(x\) is raised to the fourth power and multiplied by \(y\).
- The **denominator** is 16.
- The radical symbol indicates a seventh root, applied to the entire fraction \(\frac{x^4y}{16}\).
In an educational context, this expression showcases the use of logarithmic functions in conjunction with roots and fractions, demonstrating complex mathematical operations.
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