Logarithms of numbers may be obtained from calculators and from tables.
Example. Find each of the following. (a) ln 10. (b) log 10.
Solution: (a)
10
Displays: ln(10)
displays: 2.30259
Problem. Find (a) ln 20. (b) log 20.
Example. Use a graphing calculator to graph f (x)
= ln x, f (x) = x, and f (x)
= ex on the same set of axes.
Solution: The graphs are shown in the figure below
Note how slowly f (x) = ln x increases for x > 1. Do the graphs of all logarithmic functions pass through (1, 0)?
Note that the graphs of f (x) = ln x and f (x) = ex are reflections about the line y = x.
Problem. Use a graphing calculator to graph f (x)
= log x, f (x) = x, and f (x)
= 10x on the same set of axes.
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