BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.6, Problem 44E
To determine

To sketch: Use Formula 10 to graph the functions y=lnx,y=log10x,y=ex and y=10x on a common screen and interpret how these graphs is related.

Expert Solution

Explanation of Solution

The graphs of the function y=lnx,y=log10x,y=ex and y=10x are drawn and shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 44E

From Figure 1, it is noted that the graph y=10x is the inverse y=log10x and the y=ex is the inverse of y=lnx as they are reflection about the line y=x .

Use Formula 10, logba=lnalnb,b1 and express the function as, log10x=lnxln10 .

Thus, the graph of log10x can be obtained by vertically compressing the graph of ln x by a factor of ln 10.

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