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
Please make it is a single logarithm
![**Equation:**
Simplify the following logarithmic expression:
\[ -5 \log(z) + 8 \log(x) - 6 \log(y) = \]
**Explanation:**
In this expression, we are dealing with logarithms of different variables. The equation combines three logarithmic terms, which can be rewritten using properties of logarithms.
- The coefficients in front of the logarithms indicate the powers to which each variable will be raised (e.g., \(\log(z^5)\), \(\log(x^8)\), \(\log(y^6)\)) when applying the Power Rule for logarithms.
- The equation could be further simplified using logarithmic identities, like the Product, Quotient, and Power Rules, to form a single logarithmic expression.
The square box at the end represents a place for the simplified result or solution.
This exercise is intended to test your understanding of logarithmic identities and their applications in simplifying expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffedd89bb-46ed-48bd-b6ed-4758f981509f%2F2b005ecd-30fb-40c8-b73e-9aeb6f131f89%2Fkcikzyi_processed.png&w=3840&q=75)
Transcribed Image Text:**Equation:**
Simplify the following logarithmic expression:
\[ -5 \log(z) + 8 \log(x) - 6 \log(y) = \]
**Explanation:**
In this expression, we are dealing with logarithms of different variables. The equation combines three logarithmic terms, which can be rewritten using properties of logarithms.
- The coefficients in front of the logarithms indicate the powers to which each variable will be raised (e.g., \(\log(z^5)\), \(\log(x^8)\), \(\log(y^6)\)) when applying the Power Rule for logarithms.
- The equation could be further simplified using logarithmic identities, like the Product, Quotient, and Power Rules, to form a single logarithmic expression.
The square box at the end represents a place for the simplified result or solution.
This exercise is intended to test your understanding of logarithmic identities and their applications in simplifying expressions.
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