   Chapter 11.4, Problem 10ES ### 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. Use the definition of logarithm to show that log b b x = x for every real number x.b. Use the definition of logarithm to show that b log b x = x for every positive real number x.c. By the result of exercise 28 in Section 7.3. if f :   X → Y and g :   Y → X are functions and g ∘ f = I X and f ∘ g = I Y , then f and g are inverse functions. Use this result to show that log b and exp b , (the exponential function with base b) are inverse functions.

To determine

(a)

To prove:

Use the definition of logarithm to show that logbbx=x for all real numbers x.

Explanation

Given information:

Use the definition of logarithm to show that logbbx=x for all real numbers x.

Proof:

To prove: logbbx=x for all real numbers x

Let x be a real number and let b be a positive real number not equal to 1

To determine

(b)

To prove:

Use the definition of logarithm to show that blogbx=x for all positive real numbers x.

To determine

(c)

Use this result to show that logb and expb (the exponential function with base b ) are inverse functions.

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