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2. Solve the logarithmic equation (d) log; r = 5 (e) log2 r = -4 (f) log r = 1 %3D

2. Solve the logarithmic equation (d) log; r = 5 (e) log2 r = -4 (f) log r = 1 %3D

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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## Problem 2: Solving Logarithmic Equations ### Solve the following logarithmic equations: (d) \(\log_5 x = 5\) (e) \(\log_2 x = -4\) (f) \(\log x = 1\) ### Explanation To solve each equation, you'll need to use the property of logarithms that states: if \(\log_b x = y\), then \(b^y = x\). **For equation (d)**: - \(\log_5 x = 5\) implies that \(5^5 = x\). **For equation (e)**: - \(\log_2 x = -4\) implies that \(2^{-4} = x\). **For equation (f)**: - \(\log x = 1\) implies that \(10^1 = x\) (assuming the common logarithm with base 10). These solutions involve exponentiation, which reverses the logarithmic function to find the value of \(x\).
Transcribed Image Text:## Problem 2: Solving Logarithmic Equations ### Solve the following logarithmic equations: (d) \(\log_5 x = 5\) (e) \(\log_2 x = -4\) (f) \(\log x = 1\) ### Explanation To solve each equation, you'll need to use the property of logarithms that states: if \(\log_b x = y\), then \(b^y = x\). **For equation (d)**: - \(\log_5 x = 5\) implies that \(5^5 = x\). **For equation (e)**: - \(\log_2 x = -4\) implies that \(2^{-4} = x\). **For equation (f)**: - \(\log x = 1\) implies that \(10^1 = x\) (assuming the common logarithm with base 10). These solutions involve exponentiation, which reverses the logarithmic function to find the value of \(x\).
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