   Chapter 7.1, Problem 22ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Use the unique factorizations for the integers theorem (Section 4.4) and the definition of logaerithm to prove that log 3 (7) is irrational.

To determine

Use the unique factonzation for the integers theorem and the definition of logarithm to prove that.

log37 is irrational.

Explanation

Given information:

Let’s suppose that

log37 is rational integers.

Concept used:

Let N=3p=7q, and take its prime factorization.

As N=3p, the prime factor are all 3 and also as N=7q, the prime factors are all 7

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