   Chapter 11.4, Problem 44ES ### 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
1 views

# Prove by mathematical induction that log 2 n ≤ n for every integer n ≥ 1 .

To determine

To prove:

Prove by mathematical induction that log2nn for all integers n = 1.

Explanation

Given information:

Prove by mathematical induction that log2nn for all integers n = 1.

Proof:

PROOF BY INDUCTION:

Let P(n) be "log2nn"

Basis step: n = 1

log2n=log21=0n=1

Thus P (1) is true as 01.

Inductive step:

Let P(k) be true, thus log2kk with k2

We need to prove that P ( k + 1) is true.

log2(k+1)log2(2k)                            k+12k as k

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 