LogarithmicFunction

 Calling Sequence LogarithmicFunction(f) LogarithmicFunction(asymval, pt1, pt2)

Parameters

 f - logarithmic function in a single variable. asymval - x-value for horizontal asymptote pt1, pt2 - a GridPoint object or list/rtable representing a point on the function

Options

 • domain : a RealRange expression specifying the region over which the function is defined
 • variable: name used in generated expression when second calling sequence is used

Description

 • The LogarithmicFunction constructor generates and returns an object representing a logarithmic function. The function is assumed to have the form aln(bx+c)+d, where a, b, c and d are constants. Logarithms in different bases using the log[b] notation are supported.
 • The first calling sequence requires a logarithmic function in one variable to be provided.
 • The second calling sequence requires the value for the vertical asymptote and two points on the curve to be provided.

Examples

 > $\mathrm{with}\left(\mathrm{Grading}\right)$
 $\left[{\mathrm{AbsoluteValueFunction}}{,}{\mathrm{Draw}}{,}{\mathrm{ExponentialFunction}}{,}{\mathrm{GetData}}{,}{\mathrm{GetDomain}}{,}{\mathrm{GetExpression}}{,}{\mathrm{GradePlot}}{,}{\mathrm{GridPoint}}{,}{\mathrm{Inequalities}}{,}{\mathrm{LinearFunction}}{,}{\mathrm{LogarithmicFunction}}{,}{\mathrm{QuadraticFunction}}{,}{\mathrm{Quiz}}{,}{\mathrm{Segment}}\right]$ (1)
 > $\mathrm{LogarithmicFunction}\left(5\mathrm{log}[10]\left(2x-4\right)+5\right)$
 ${\mathrm{<< LogarithmicFunction: 5*ln\left(2*x-4\right)/ln\left(10\right)+5>>}}$ (2)
 > $\mathrm{LogarithmicFunction}\left(2,\left[3,6.5\right],\left[4,8\right]\right)$
 ${\mathrm{<< LogarithmicFunction: 1.5/ln\left(2\right)*ln\left(v-2\right)+6.5>>}}$ (3)
 > $\mathrm{L1}≔\mathrm{LogarithmicFunction}\left(3,\left[4,0\right],\left[6,\mathrm{ln}\left(3\right)\right],'\mathrm{variable}'='z'\right)$
 ${\mathrm{L1}}{:=}{\mathrm{<< LogarithmicFunction: ln\left(z-3\right)>>}}$ (4)
 > $\mathrm{GetExpression}\left(\mathrm{L1}\right)$
 ${\mathrm{ln}}{}\left({z}{-}{3}\right){,}{z}$ (5)

Compatibility

 • The Grading:-LogarithmicFunction command was introduced in Maple 18.