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log 5 + log (x + 8) = 2

log 5 + log (x + 8) = 2

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
The equation shown is: \[ \log 5 + \log (x + 8) = 2 \] This equation involves logarithms, an important concept in mathematics. It can be simplified by using the logarithmic property that states: \[ \log a + \log b = \log (ab) \] Therefore, the equation can be rewritten as: \[ \log [5(x + 8)] = 2 \] This implies: \[ 5(x + 8) = 10^2 \] Since \(\log a = b\) means \(a = 10^b\) when the base is 10. Solving this equation will give the value of \(x\).
Transcribed Image Text:The equation shown is: \[ \log 5 + \log (x + 8) = 2 \] This equation involves logarithms, an important concept in mathematics. It can be simplified by using the logarithmic property that states: \[ \log a + \log b = \log (ab) \] Therefore, the equation can be rewritten as: \[ \log [5(x + 8)] = 2 \] This implies: \[ 5(x + 8) = 10^2 \] Since \(\log a = b\) means \(a = 10^b\) when the base is 10. Solving this equation will give the value of \(x\).
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