   Chapter 11.5, Problem 1ES ### 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

# Use the facts that log 2   10 ≅ 3.32 and that for each real number a ,   log 2 ( 10 a ) = a   log 2   10 to find log 2 ( 1 , 000 ) ,   log 2 ( 1 , 000 , 000 ) , and log 2 ( 1 , 000 , 000 , 000 , 000 ) .

To determine

Find log2 (1, 000),log2 (1, 000, 000), and log2(1, 000, 000, 000, 000).

Explanation

Given information:

Use the facts that log2103.32 and that for all real numbers a, log2(10a)=alog210

Calculation:

Given::

log2103.32

log210a=alog210 for all real numbers a

Using that 1000 = 103:

log21000=log2103

=3log210                                  log210a=alog210

33.32                                            log2103.32

=9.96

Using that 1,000,000 = 106:

log21,000,000=log2106

=6log210                            log210a=alog210

63

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