   Chapter 11.4, Problem 14ES ### 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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# a. Prove that if x is a positive real number and k is a nonnegative integer such that 2 k − 1 < x ≤ 2 k , then ⌈ log 2 x ⌉ = k .b. Describe in words the statement proved in part (a).

To determine

(a)

Prove that if x is a positive real number and k is a nonnegative integer such that 2k1<x2k, then log2x=k.

Explanation

Given information:

x is a positive real number and k is a nonnegative integer such that 2k1<x2k.

Proof:

Suppose that k is an integer and x is a real number with

2k1<x2k

Since the logarithmic function with base 2 is an increasing function, therefore,

log2(2k1)<log2xlog2(</

To determine

(b)

Describe in words the statement proved in part (a).

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