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 f⇔u=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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Chapter 11 Solutions

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Sect-11.1 P-1TY Sect-11.1 P-2TY Sect-11.1 P-3TY Sect-11.1 P-4TY Sect-11.1 P-5TY Sect-11.1 P-6TY Sect-11.1 P-1ES Sect-11.1 P-2ES Sect-11.1 P-3ES Sect-11.1 P-4ES

Sect-11.1 P-5ES Sect-11.1 P-6ES Sect-11.1 P-7ES Sect-11.1 P-8ES Sect-11.1 P-9ES Sect-11.1 P-10ES Sect-11.1 P-11ES Sect-11.1 P-12ES Sect-11.1 P-13ES Sect-11.1 P-14ES Sect-11.1 P-15ES Sect-11.1 P-16ES Sect-11.1 P-17ES Sect-11.1 P-18ES Sect-11.1 P-19ES Sect-11.1 P-20ES Sect-11.1 P-21ES Sect-11.1 P-22ES Sect-11.1 P-23ES Sect-11.1 P-24ES Sect-11.1 P-25ES Sect-11.1 P-26ES Sect-11.1 P-27ES Sect-11.1 P-28ES Sect-11.2 P-1TY Sect-11.2 P-2TY Sect-11.2 P-3TY Sect-11.2 P-4TY Sect-11.2 P-5TY Sect-11.2 P-6TY Sect-11.2 P-1ES Sect-11.2 P-2ES Sect-11.2 P-3ES Sect-11.2 P-4ES Sect-11.2 P-5ES Sect-11.2 P-6ES Sect-11.2 P-7ES Sect-11.2 P-8ES Sect-11.2 P-9ES Sect-11.2 P-10ES Sect-11.2 P-11ES Sect-11.2 P-12ES Sect-11.2 P-13ES Sect-11.2 P-14ES Sect-11.2 P-15ES Sect-11.2 P-16ES Sect-11.2 P-17ES Sect-11.2 P-18ES Sect-11.2 P-19ES Sect-11.2 P-20ES Sect-11.2 P-21ES Sect-11.2 P-22ES Sect-11.2 P-23ES Sect-11.2 P-24ES Sect-11.2 P-25ES Sect-11.2 P-26ES Sect-11.2 P-27ES Sect-11.2 P-28ES Sect-11.2 P-29ES Sect-11.2 P-30ES Sect-11.2 P-31ES Sect-11.2 P-32ES Sect-11.2 P-33ES Sect-11.2 P-34ES Sect-11.2 P-35ES Sect-11.2 P-36ES Sect-11.2 P-37ES Sect-11.2 P-38ES Sect-11.2 P-39ES Sect-11.2 P-40ES Sect-11.2 P-41ES Sect-11.2 P-42ES Sect-11.2 P-43ES Sect-11.2 P-44ES Sect-11.2 P-45ES Sect-11.2 P-46ES Sect-11.2 P-47ES Sect-11.2 P-48ES Sect-11.2 P-49ES Sect-11.2 P-50ES Sect-11.2 P-51ES Sect-11.3 P-1TY Sect-11.3 P-2TY Sect-11.3 P-3TY Sect-11.3 P-1ES Sect-11.3 P-2ES Sect-11.3 P-3ES Sect-11.3 P-4ES Sect-11.3 P-5ES Sect-11.3 P-6ES Sect-11.3 P-7ES Sect-11.3 P-8ES Sect-11.3 P-9ES Sect-11.3 P-10ES Sect-11.3 P-11ES Sect-11.3 P-12ES Sect-11.3 P-13ES Sect-11.3 P-14ES Sect-11.3 P-15ES Sect-11.3 P-16ES Sect-11.3 P-17ES Sect-11.3 P-18ES Sect-11.3 P-19ES Sect-11.3 P-20ES Sect-11.3 P-21ES Sect-11.3 P-22ES Sect-11.3 P-23ES Sect-11.3 P-24ES Sect-11.3 P-25ES Sect-11.3 P-26ES Sect-11.3 P-27ES Sect-11.3 P-28ES Sect-11.3 P-29ES Sect-11.3 P-30ES Sect-11.3 P-31ES Sect-11.3 P-32ES Sect-11.3 P-33ES Sect-11.3 P-34ES Sect-11.3 P-35ES Sect-11.3 P-36ES Sect-11.3 P-37ES Sect-11.3 P-38ES Sect-11.3 P-39ES Sect-11.3 P-40ES Sect-11.3 P-41ES Sect-11.3 P-42ES Sect-11.3 P-43ES Sect-11.4 P-1TY Sect-11.4 P-2TY Sect-11.4 P-3TY Sect-11.4 P-4TY Sect-11.4 P-5TY Sect-11.4 P-1ES Sect-11.4 P-2ES Sect-11.4 P-3ES Sect-11.4 P-4ES Sect-11.4 P-5ES Sect-11.4 P-6ES Sect-11.4 P-7ES Sect-11.4 P-8ES Sect-11.4 P-9ES Sect-11.4 P-10ES Sect-11.4 P-11ES Sect-11.4 P-12ES Sect-11.4 P-13ES Sect-11.4 P-14ES Sect-11.4 P-15ES Sect-11.4 P-16ES Sect-11.4 P-17ES Sect-11.4 P-18ES Sect-11.4 P-19ES Sect-11.4 P-20ES Sect-11.4 P-21ES Sect-11.4 P-22ES Sect-11.4 P-23ES Sect-11.4 P-24ES Sect-11.4 P-25ES Sect-11.4 P-26ES Sect-11.4 P-27ES Sect-11.4 P-28ES Sect-11.4 P-29ES Sect-11.4 P-30ES Sect-11.4 P-31ES Sect-11.4 P-32ES Sect-11.4 P-33ES Sect-11.4 P-34ES Sect-11.4 P-35ES Sect-11.4 P-36ES Sect-11.4 P-37ES Sect-11.4 P-38ES Sect-11.4 P-39ES Sect-11.4 P-40ES Sect-11.4 P-41ES Sect-11.4 P-42ES Sect-11.4 P-43ES Sect-11.4 P-44ES Sect-11.4 P-45ES Sect-11.4 P-46ES Sect-11.4 P-47ES Sect-11.4 P-48ES Sect-11.4 P-49ES Sect-11.4 P-50ES Sect-11.4 P-51ES Sect-11.5 P-1TY Sect-11.5 P-2TY Sect-11.5 P-3TY Sect-11.5 P-4TY Sect-11.5 P-5TY Sect-11.5 P-1ES Sect-11.5 P-2ES Sect-11.5 P-3ES Sect-11.5 P-4ES Sect-11.5 P-5ES Sect-11.5 P-6ES Sect-11.5 P-7ES Sect-11.5 P-8ES Sect-11.5 P-9ES Sect-11.5 P-10ES Sect-11.5 P-11ES Sect-11.5 P-12ES Sect-11.5 P-13ES Sect-11.5 P-14ES Sect-11.5 P-15ES Sect-11.5 P-16ES Sect-11.5 P-17ES Sect-11.5 P-18ES Sect-11.5 P-19ES Sect-11.5 P-20ES Sect-11.5 P-21ES Sect-11.5 P-22ES Sect-11.5 P-23ES Sect-11.5 P-24ES Sect-11.5 P-25ES Sect-11.5 P-26ES

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