EML Function

Author

Eric W. Weisstein
May 24, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/SpecialFunctions/EMLFunction.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/EMLFunction.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Function

EMLFunction[x_,y_]:=Exp[x]-Log[y]

Plot

exp(x)-y plane

plot1=ContourPlot[Exp[x]-u,{x,-3,2.5},{u,-3,3},Contours->Range[-4,14,2],ContourLabels->True,ColorFunction->Hue,FrameLabel->{x,Row[{"ln",
Style["y",Italic]}," "]},PlotPoints->60,MaxRecursion->2]

x-y plane

plot2=ContourPlot[EMLFunction[x,y],{x,-3,2.5},{y,0.05,8},Contours->Range[-2,14,2],ContourLabels->True,ColorFunction->Hue,PlotPoints->80,MaxRecursion->2,FrameLabel->{x,y}]

3D

plot3=Plot3D[EMLFunction[x,y],{x,-4,4},{y,0,1},ClippingStyle->None,AxesLabel->{x,y},BaseStyle->Directive[FontFamily->"Times",12],MaxRecursion->0,PlotStyle->Opacity[.6]]

Combined

GraphicsRow[{plot1,plot2,plot3},
BaseStyle->InsetBoxOptions->{BaseStyle->Directive[14,FontFamily->"Times"]}
]