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
Expand the following logarithms so that they contain no products, quotients, or powers.
![The expression is a mathematical logarithmic function:
\[ \ln \left[ \frac{e^4 \sqrt{x} - 5}{(7x - e)^{2/3}} \right] \]
Here, \(\ln\) represents the natural logarithm, \(e\) is Euler's number (approximately 2.718), and \(x\) is a variable. The expression inside the logarithm is a fraction with the following components:
- **Numerator:** \(e^4 \sqrt{x} - 5\)
- \(e^4\) indicates \(e\) raised to the power of 4.
- \(\sqrt{x}\) denotes the square root of \(x\).
- The whole expression is reduced by 5.
- **Denominator:** \((7x - e)^{2/3}\)
- \(7x - e\) represents the expression within the binomial.
- The expression is raised to the power of \(2/3\), indicating a cube root squared transformation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff91ef73-4530-48ba-be88-fd15c629792d%2F8c6d91a7-3ee3-4cac-bd54-bad544bb4b15%2Feobmaq_processed.png&w=3840&q=75)
Transcribed Image Text:The expression is a mathematical logarithmic function:
\[ \ln \left[ \frac{e^4 \sqrt{x} - 5}{(7x - e)^{2/3}} \right] \]
Here, \(\ln\) represents the natural logarithm, \(e\) is Euler's number (approximately 2.718), and \(x\) is a variable. The expression inside the logarithm is a fraction with the following components:
- **Numerator:** \(e^4 \sqrt{x} - 5\)
- \(e^4\) indicates \(e\) raised to the power of 4.
- \(\sqrt{x}\) denotes the square root of \(x\).
- The whole expression is reduced by 5.
- **Denominator:** \((7x - e)^{2/3}\)
- \(7x - e\) represents the expression within the binomial.
- The expression is raised to the power of \(2/3\), indicating a cube root squared transformation.
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