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35) logs 3

35) logs 3

Calculus: Early Transcendentals
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 logarithm
Certainly! Here is a transcription of the text from the image along with an explanation: --- **Transcription:** 1. \(6 \log_{3} 7 + \log 2\) 2. \(35) \log_{5} \left( \frac{x}{y^3} \right)^3\) --- **Explanation:** 1. **Expression:** \(6 \log_{3} 7 + \log 2\) - This expression involves logarithms with different bases. The first term, \(6 \log_{3} 7\), represents the logarithm of 7 with base 3, multiplied by 6. The second term, \(\log 2\), is a logarithm with an unspecified base (commonly assumed to be base 10 if not specified). 2. **Expression:** \(35) \log_{5} \left( \frac{x}{y^3} \right)^3\) - This expression includes a logarithm with base 5. The argument of the logarithm is a fraction raised to the third power, where the numerator is \(x\) and the denominator is \(y^3\). The notation \(\left( \frac{x}{y^3} \right)^3\) indicates that the entire fraction \(\frac{x}{y^3}\) is cubed. These expressions are commonly encountered in mathematics, particularly in algebra and calculus, where the properties and laws of logarithms are often used to simplify or solve equations.
Transcribed Image Text:Certainly! Here is a transcription of the text from the image along with an explanation: --- **Transcription:** 1. \(6 \log_{3} 7 + \log 2\) 2. \(35) \log_{5} \left( \frac{x}{y^3} \right)^3\) --- **Explanation:** 1. **Expression:** \(6 \log_{3} 7 + \log 2\) - This expression involves logarithms with different bases. The first term, \(6 \log_{3} 7\), represents the logarithm of 7 with base 3, multiplied by 6. The second term, \(\log 2\), is a logarithm with an unspecified base (commonly assumed to be base 10 if not specified). 2. **Expression:** \(35) \log_{5} \left( \frac{x}{y^3} \right)^3\) - This expression includes a logarithm with base 5. The argument of the logarithm is a fraction raised to the third power, where the numerator is \(x\) and the denominator is \(y^3\). The notation \(\left( \frac{x}{y^3} \right)^3\) indicates that the entire fraction \(\frac{x}{y^3}\) is cubed. These expressions are commonly encountered in mathematics, particularly in algebra and calculus, where the properties and laws of logarithms are often used to simplify or solve equations.
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