   Chapter 11.4, Problem 11ES ### 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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# Let b > 1 . a. Use the fact that u = log b   v ⇔ v = b u to show that a point (u, v) lies on the graph of the logarithinic function with base b if, and only if, (v, u) lies on the graph of the exponential function with base b.b. Plot several pairs of points of the form (u, v) and (v, u) on a coordinate system. Describe the geometric relationship between the locations of the points in each pair.c. Draw the graphs of y = log 2 x and y = 2 x . Describe the geometric relationship between these graphs.

To determine

(a)

To proof that (u, v) lies on the graph of the logarithmic function with base b if and only (u, v) lies on the graph of the exponential fraction with base b by using the definition of a logarithm.

Explanation

a)As given in the problem that (u, v) lies on the graph of the logarithmic function with base b if and only (u, v) lies on the graph of the exponential fraction with base b by using the definition of a logarithm.

(u,v)is point lies on the graph of fu=f(v)u=logbx<

To determine

(b)

To proof that (u, v) lies on the graph of the logarithmic function with base b if and only (u, v) lies on the graph of the exponential fraction with base b by using the definition of a logarithm.

To determine

(c)

To proof that (u, v) lies on the graph of the logarithmic function with base b if and only (u, v) lies on the graph of the exponential fraction with base b by using the definition of a logarithm.

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