   Chapter 7.2, Problem 35ES ### 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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# The properties of logarithm established in 33-35 are used in Sections 11.4 and 11.5. Prove that for all real numbers a, b, and x with b and x positive and b ≠ 1 , log b ( x a ) = a log b x .

To determine

To prove that logb(x)a=alogbx for all real numbers a,b and x with b and x positive and b1 ,

Explanation

Given information:

a,

b,x,y are all positive real numbers.

Concept used:

logab=cb=ac

Proof:

Let a,b and x are positive real numbers and b1.

Suppose that logb(x)a=m

Recall the fact that, for each positive real number s and real number t.

logbs=tbt=s..........(1)

As logb(x)a=m get bm=xa [By the fact (1) ]

( b m)

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