**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.

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.

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.

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

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