   Chapter 11.4, Problem 41ES ### 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

# Show that ⌊ log 2 n ⌋ is Θ ( log 2 n ) .

To determine

(a)

Show that log2n is Θ(log2n).

Explanation

Given information:

log2n

Proof:

By the definition of the floor function: xx for all real numbers x.

|log2n||log2n| whenever n0

By the definition of the floor function: x1<xx for all real numbers x and when n4 then n2n.

|log2n||log2n1|

=|log2nlog22|

=|log2n2|                              logbxy=logbxlogby

|log2n|                                                   n2n

To determine

(b)

Show that log2n+1 is Θ(log2n).

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