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6 log(x² – 81)–12[log(x+9)–3log(x)]

6 log(x² – 81)–12[log(x+9)–3log(x)]

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question

Contract the expression into a single logarithm with coefficient of 1. Simply completely. 

The mathematical expression is: \[ 6 \log(x^2 - 81) - 12 \left[ \log(x + 9) - 3 \log(x) \right] \] This expression involves logarithmic functions, which are commonly used in algebra to solve equations involving exponentials. The expression breaks down as a combination of logarithms with different arguments and coefficients, utilizing properties such as the log of a product, quotient, and powers. The specific terms are: - \( 6 \log(x^2 - 81) \): This term represents six times the logarithm of \( x^2 \) minus 81. - \( -12 \left[ \log(x + 9) - 3 \log(x) \right] \): This portion begins with a multiplication of -12 and involves the subtraction of \( \log(x+9) \) and three times \( \log(x) \). Understanding how to manipulate and simplify such expressions is essential in solving complex logarithmic equations in higher-level mathematics.
Transcribed Image Text:The mathematical expression is: \[ 6 \log(x^2 - 81) - 12 \left[ \log(x + 9) - 3 \log(x) \right] \] This expression involves logarithmic functions, which are commonly used in algebra to solve equations involving exponentials. The expression breaks down as a combination of logarithms with different arguments and coefficients, utilizing properties such as the log of a product, quotient, and powers. The specific terms are: - \( 6 \log(x^2 - 81) \): This term represents six times the logarithm of \( x^2 \) minus 81. - \( -12 \left[ \log(x + 9) - 3 \log(x) \right] \): This portion begins with a multiplication of -12 and involves the subtraction of \( \log(x+9) \) and three times \( \log(x) \). Understanding how to manipulate and simplify such expressions is essential in solving complex logarithmic equations in higher-level mathematics.
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