Introduction to Algebra using the TI-92 Ó 1997
by Nathan O. Niles
Associate Professor (Retired)
U. S. Naval Academy


13. Logarithms

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

log  10   Displays: 1

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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