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
![**Problem: Find the Logarithm**
The expression given is:
\[
\log\left(\frac{1}{100,000}\right) = \, \text{(Insert Answer Here)}
\]
**Explanation:**
To find the logarithm of a fraction, especially \(\log\left(\frac{1}{100,000}\right)\), you can use the properties of logarithms. Notice that 100,000 can be written as \(10^5\), so:
\[
\frac{1}{100,000} = 10^{-5}
\]
Thus, the expression becomes:
\[
\log\left(10^{-5}\right)
\]
Using the logarithmic identity \(\log(a^b) = b \log(a)\), where \(a = 10\) and \(b = -5\), the evaluation is:
\[
\log\left(10^{-5}\right) = -5
\]
Therefore, the solution to the original problem is:
\[
\log\left(\frac{1}{100,000}\right) = -5
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76447b6-9a79-40f3-b9ba-1d0612675f50%2F894c1c02-1fa1-43a6-9911-e465ca972678%2Fkntgbgn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Find the Logarithm**
The expression given is:
\[
\log\left(\frac{1}{100,000}\right) = \, \text{(Insert Answer Here)}
\]
**Explanation:**
To find the logarithm of a fraction, especially \(\log\left(\frac{1}{100,000}\right)\), you can use the properties of logarithms. Notice that 100,000 can be written as \(10^5\), so:
\[
\frac{1}{100,000} = 10^{-5}
\]
Thus, the expression becomes:
\[
\log\left(10^{-5}\right)
\]
Using the logarithmic identity \(\log(a^b) = b \log(a)\), where \(a = 10\) and \(b = -5\), the evaluation is:
\[
\log\left(10^{-5}\right) = -5
\]
Therefore, the solution to the original problem is:
\[
\log\left(\frac{1}{100,000}\right) = -5
\]
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