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Is the base 2 logarithm of 3, log₂ 3, a rational number or an irrational number? Justify your conclusion.

Is the base 2 logarithm of 3, log₂ 3, a rational number or an irrational number? Justify your conclusion.

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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For this question I don't understand for the solution given how you found log_2(3) to be rational... can you explain and show using (mod#)?

 

**(b) Is the base 2 logarithm of 3, \( \log_2 3 \), a rational number or an irrational number? Justify your conclusion.** This question explores whether \( \log_2 3 \) is a rational or irrational number. To justify the conclusion, consider the properties of logarithms and the definitions of rational and irrational numbers.
Transcribed Image Text:**(b) Is the base 2 logarithm of 3, \( \log_2 3 \), a rational number or an irrational number? Justify your conclusion.** This question explores whether \( \log_2 3 \) is a rational or irrational number. To justify the conclusion, consider the properties of logarithms and the definitions of rational and irrational numbers.
Expert Solution
Step 1: Given

Algebra homework question answer, step 1, image 1

Formula :

a(logb) = log (ba)

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