Logarithms - Change of Base

• When working with logarithms, we sometimes want to enter the log into the calculator. If the base is 10 or e, this is done with a simple key stroke, LOG for log base 10, and LN for log base e (natural log).

• To enter a log to a base other than 10 or e, use the change of base formula:

blog

MlogMlog

a

ab

• Select base “a” to be either 10 or e.

Slide 2

Logarithms - Change of Base

• Example 1:

Enter log512 into the calculator using base 10.

Press ENTER to evaluate.

5LOG

12LOG

5log

12log12log

10

105

Slide 3

Logarithms - Change of Base

• Example 2:

Enter log512 into the calculator using base e.

Press ENTER to evaluate.

5LN

12LN

5log

12log12log

e

e5

• Note that the new base is arbitrary. The same answer resulted using base 10 and base e.

Slide 4

• Example 3:

Logarithms - Change of Base

Sketch the graph of )2x(logy 7

7ln

)2x(ln)2x(logy 7

Type the function into Y1

Select the ZOOM|ZStandard window.

Slide 5

Logarithms - Change of Base

For a better window, press WINDOW and make the following changes:

Press GRAPH to obtain ...

Note that there is a vertical asymptote at x = 2

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