Graphing a Logarithmic Function

Graph:

1. \(f( x) =\log _{2}x\)
2. \(g( x) =\log _{1/3}x\)
3. \(F( x) =\ln x\)

Solution (a) To graph \(f( x) =\log _{2}x\), graph \( y=2^{x}\) and reflect it about the line \(y=x.\) See Figure 66(a).

(b) To graph \(f( x) =\log _{1/3}x\), graph \( y=\left( \dfrac{1}{3}\!\right) ^{\!\!\!x}\) and reflect it about the line \(y=x.\) See Figure 66(b).

(c) To graph \(F( x) =\ln x\), graph \(y=e^{x}\) and reflect it about the line \(y=x\). See Figure 66(c).