   Chapter 7.2, Problem 33ES ### 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 positive real numbers b, x, and y with b ≠ 1 . log b ( x y ) = log b x − log b y .

To determine

To prove that logb(xy)=logbxlogby for all positive real numbers b,x and y with b1.

Explanation

Given information:

b,x,y are all positive real numbers.

Concept used:

logab=cb=ac

Proof:

Let b1 be a positive integer.

Suppose that logbx=m,logby=n.

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

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

As logbx=m, get bm=x [By the fact (1) ]

As logby=n, get bn=y [By the fact

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