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 43E
To determine

To sketch: Use Formula 10 to graph the functions y=log1.5x,y=lnx,y=log10x and y=log50x on a common screen and interpret how these graphs is related.

Expert Solution

Explanation of Solution

The graphs of the function y=log1.5x,y=lnx,y=log10x and y=log50x are drawn and shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 43E

From Figure 1, it is noted that the graphs are passing through the common point (1, 0).

Use Formula 10, logba=lnalnb,b1 and express the given log function in terms of natural logarithm (ln) and identify the relationship between each graph.

log1.5x=lnxln1.5log10x=lnxln10log50x=lnxln50

Thus, the given graphs are related in a such a way that y=lnx times the factor, y=1ln(base) .

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