Chapter 1, Problem 14P

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Use indirect reasoning to prove that log_{2} 5 is an irrational number.

To determine

**To prove:**

Explanation

**Definition used:**

*Logarithmic function*

A function such as

**Proof:**

Suppose

Rational number is the form *p,q* is a natural number.

*p* and *q.*

By definition of logarithmic function,

The right hand side

No two natural numbers satisfy above equation.

Therefore, this is a contradiction to the assumption (1).

Thus,

Hence the result.

Sect-1.1 P-1ESect-1.1 P-2ESect-1.1 P-3ESect-1.1 P-4ESect-1.1 P-5ESect-1.1 P-7ESect-1.1 P-8ESect-1.1 P-9ESect-1.1 P-10ESect-1.1 P-11E

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