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Logarithm and Exponential Graphing Help

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By — McGraw-Hill Professional
Updated on Aug 31, 2011

Logarithm and Exponential Graphing

If a > 0 and f(x) = log a x, x > 0, then

Using this information, we can sketch the graph of f ( x ) = log a x .

If a > 1 then ln a > 0 so that f′ ( x ) > 0 and f″ ( x ) < 0. The graph of f is exhibited in Fig. 6.6.

Fig. 6.6

If 0 < a < 1 then ln a = − ln(1/ a ) < 0 so that f′ ( x ) < 0 and f″ ( x ) > 0. The graph of f is sketched in Fig. 6.7.

Since g ( x ) = a x is the inverse function to f ( x ) = log a x , the graph of g is the reflection in the line y = x of the graph of f (Figs 6.6 and 6.7). See Figs 6.8, 6.9.

Fig. 6.7

Fig. 6.8

Fig. 6.9

Figure 6.10 shows the graphs of log a x for several different values of a > 1.

Figure 6.11 shows the graphs of a x for several different values of a > 1.

You Try It : Sketch the graph of y = 4 x and y = log 4 x on the same set of axes.

Fig. 6.10

Fig. 6.11

Find practice problems and solutions for these concepts at: Transcendental Functions Practice Test.

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