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 Statement:**
Find the logarithm.
\[ \log_2 \left(\frac{1}{16}\right) = \square \]
**Explanation:**
You are tasked with finding the base 2 logarithm of the fraction \(\frac{1}{16}\). This requires determining the exponent to which the base, 2, must be raised to yield the number \(\frac{1}{16}\).
**Calculation Step-By-Step:**
1. Express \(16\) as a power of \(2\):
\[
16 = 2^4
\]
2. Therefore, \(\frac{1}{16} = 2^{-4}\).
3. So, \(\log_2 \left(\frac{1}{16}\right) = \log_2 (2^{-4}) = -4 \).
The answer is \(-4\).
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Transcribed Image Text:**Problem Statement:**
Find the logarithm.
\[ \log_2 \left(\frac{1}{16}\right) = \square \]
**Explanation:**
You are tasked with finding the base 2 logarithm of the fraction \(\frac{1}{16}\). This requires determining the exponent to which the base, 2, must be raised to yield the number \(\frac{1}{16}\).
**Calculation Step-By-Step:**
1. Express \(16\) as a power of \(2\):
\[
16 = 2^4
\]
2. Therefore, \(\frac{1}{16} = 2^{-4}\).
3. So, \(\log_2 \left(\frac{1}{16}\right) = \log_2 (2^{-4}) = -4 \).
The answer is \(-4\).
**Navigation:**
To proceed to the next task, click on the "Next Question" button.
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