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Wolfram Language & System Documentation Center
LogLogPlot
  • See Also
    • ListLogLogPlot
    • LogPlot
    • LogLinearPlot
    • Plot
    • ParametricPlot
  • Related Guides
    • Function Visualization
  • Tech Notes
    • Some Special Plots
    • See Also
      • ListLogLogPlot
      • LogPlot
      • LogLinearPlot
      • Plot
      • ParametricPlot
    • Related Guides
      • Function Visualization
    • Tech Notes
      • Some Special Plots

LogLogPlot[f,{x,xmin,xmax}]

generates a log-log plot of f as a function of x from xmin to xmax.

LogLogPlot[{f1,f2,…},{x,xmin,xmax}]

plots several functions fi.

LogLogPlot[{…,w[fi],…},…]

plots fi with features defined by the symbolic wrapper w.

LogLogPlot[…,{x}∈reg]

takes the variable x to be in the geometric region reg.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Sampling  
Labeling and Legending  
Presentation  
Options  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
Show More Show More
EvaluationMonitor  
Exclusions  
ExclusionsStyle  
Filling  
FillingStyle  
LabelingSize  
MaxRecursion  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
PerformanceGoal  
PlotHighlighting  
PlotInteractivity  
PlotLabel  
PlotLabels  
PlotLayout  
PlotLegends  
PlotPoints  
PlotRange  
PlotStyle  
PlotTheme  
RegionFunction  
ScalingFunctions  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ListLogLogPlot
    • LogPlot
    • LogLinearPlot
    • Plot
    • ParametricPlot
  • Related Guides
    • Function Visualization
  • Tech Notes
    • Some Special Plots
    • See Also
      • ListLogLogPlot
      • LogPlot
      • LogLinearPlot
      • Plot
      • ParametricPlot
    • Related Guides
      • Function Visualization
    • Tech Notes
      • Some Special Plots

LogLogPlot

LogLogPlot[f,{x,xmin,xmax}]

generates a log-log plot of f as a function of x from xmin to xmax.

LogLogPlot[{f1,f2,…},{x,xmin,xmax}]

plots several functions fi.

LogLogPlot[{…,w[fi],…},…]

plots fi with features defined by the symbolic wrapper w.

LogLogPlot[…,{x}∈reg]

takes the variable x to be in the geometric region reg.

Details and Options

  • LogLogPlot makes power-law functions appear as straight lines. It allows very small or very large value changes to be seen over very large domains.
  • LogLogPlot effectively generates a curve in which Log[f] is plotted against Log[x], but with tick marks indicating the original values of f and x. It visualizes the set .
  • Gaps are left at any x where the fi evaluate to anything other than positive real numbers or
    Quantity.
  • The limits xmin and xmax can be real numbers or Quantity expressions.
  • The region reg can be any RegionQ object in 1D.
  • LogLogPlot treats the variable x as local, effectively using Block.
  • LogLogPlot has attribute HoldAll and evaluates f only after assigning specific numerical values to x.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x.
  • The following wrappers w can be used for the fi:
  • Annotation[fi,label]provide an annotation for the fi
    Button[fi,action]evaluate action when the curve for fi is clicked
    Callout[fi,label]label the function with a callout
    Callout[fi,label,pos]place the callout at relative position pos
    EventHandler[fi,events]define a general event handler for fi
    Highlighted[fi,effect]dynamically highlight fi with an effect
    Highlighted[fi,Placed[effect,pos]]statically highlight fi with an effect at position pos
    Hyperlink[fi,uri]make the function a hyperlink
    Labeled[fi,label]label the function
    Labeled[fi,label,pos]place the label at relative position pos
    Legended[fi,label]identify the function in a legend
    PopupWindow[fi,cont]attach a popup window to the function
    StatusArea[fi,label]display in the status area on mouseover
    Style[fi,styles]show the function using the specified styles
    Tooltip[fi,label]attach a tooltip to the function
    Tooltip[fi]use functions as tooltips
  • Wrappers w can be applied at multiple levels:
  • w[fi]wrap the fi
    w[{f1,…}]wrap a collection of fi
    w1[w2[…]]use nested wrappers
  • Callout, Labeled, and Placed can use the following positions pos:
  • Automaticautomatically placed labels
    Above, Below, Before, Afterpositions around the curve
    xnear the curve at a position x
    Scaled[s]scaled position s along the curve
    {s,Above},{s,Below},…relative position at position s along the curve
    {pos,epos}epos in label placed at relative position pos of the curve
  • LogLogPlot has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio1/GoldenRatioratio of height to width
    AxesTruewhether to draw axes
    ClippingStyle Nonewhat to draw where curves are clipped
    ColorFunction Automatichow to determine the coloring of curves
    ColorFunctionScaling Truewhether to scale arguments to ColorFunction
    EvaluationMonitor Noneexpression to evaluate at every function evaluation
    Exclusions Automaticpoints in x to exclude
    ExclusionsStyle Nonewhat to draw at excluded points
    Filling Nonefilling to insert under each curve
    FillingStyle Automaticstyle to use for filling
    LabelingSize Automaticmaximum size of callouts and labels
    MaxRecursion Automaticthe maximum number of recursive subdivisions allowed
    Mesh Nonehow many mesh points to draw on each curve
    MeshFunctions {#1&}how to determine the placement of mesh points
    MeshShading Nonehow to shade regions between mesh points
    MeshStyle Automaticthe style for mesh points
    MethodAutomaticthe method to use for refining curves
    PerformanceGoal $PerformanceGoalaspects of performance to try to optimize
    PlotHighlighting Automatichighlighting effect for curves
    PlotInteractivity $PlotInteractivitywhether to allow interactive elements
    PlotLabel Noneoverall label for the plot
    PlotLabels Nonelabels to use for curves
    PlotLegends Nonelegends for curves
    PlotPoints Automaticinitial number of sample points
    PlotRange {Full,Automatic}the range of y or other values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyle Automaticgraphics directives to specify the style for each curve
    PlotTheme $PlotThemeoverall theme for the plot
    RegionFunction (True&)how to determine whether a point should be included
    ScalingFunctions Nonehow to scale individual coordinates
    TargetUnitsAutomaticunits to display in the plot
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • Possible settings for ClippingStyle are:
  • Automaticuse a dotted line for the clipped portion
    Noneomit the clipped portion of the curve
    styleuse style for the clipped portion
  • Possible settings for PlotLayout that show single curves in multiple plot panels include:
  • "Column"use separate curves in a column of panels
    "Row"use separate curves in a row of panels
    {"Column",k},{"Row",k}use k columns or rows
    {"Column",UpTo[k]},{"Row",UpTo[k]}use at most k columns or rows
  • With the default settings Exclusions->Automatic and ExclusionsStyle->None, LogLogPlot breaks curves at discontinuities and singularities it detects. Exclusions->None joins across discontinuities and singularities.
  • Exclusions->{x1,x2,…} is equivalent to Exclusions->{x==x1,x==x2,…}.
  • PlotLegends->"Expressions" uses the fi as the legend text.
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • Possible highlighting effects for Highlighted and PlotHighlighting include:
  • stylehighlight the indicated curve
    "Ball"highlight and label the indicated point in a curve
    "Dropline"highlight and label the indicated point in a curve with droplines to the axes
    "XSlice"highlight and label all points along a vertical slice
    "YSlice"highlight and label all points along a horizontal slice
    Placed[effect,pos]statically highlight the given position pos
  • Highlight position specifications pos include:
  • x, {x}effect at {x,y} with y chosen automatically
    {x,y}effect at {x,y}
    {pos1,pos2,…}multiple positions posi
  • LogLogPlot initially evaluates f at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
  • Since only a finite number of sample points are used, it is possible for LogLogPlot to miss features of f. Increasing the settings for PlotPoints and MaxRecursion will often catch such features.
  • Themes that affect curves include:
  • "ThinLines"thin plot lines
    "MediumLines"medium plot lines
    "ThickLines"thick plot lines
  • The arguments supplied to functions in MeshFunctions and RegionFunction are x, y. Functions in ColorFunction are by default supplied with scaled versions of these arguments.
  • Possible settings for ScalingFunctions include:
  • syscale the y axis
    {sx,sy}scale x and y axes
  • Common built-in scaling functions s include:
  • "Log"log scale with automatic tick labeling
    "Log10"base-10 log scale with powers of 10 for ticks
    "SignedLog"log-like scale that includes 0 and negative numbers
    "Reverse"reverse the coordinate direction
    "Infinite"infinite scale
  • If a scaling function is specified for either direction, it is applied after the normal log scaling.
  • List of all options
  • Highlight options with settings specific to LogLogPlot
  • AlignmentPointCenterthe default point in the graphic to align with
    AspectRatio1/GoldenRatioratio of height to width
    AxesTruewhether to draw axes
    AxesLabelNoneaxes labels
    AxesOriginAutomaticwhere axes should cross
    AxesStyle{}style specifications for the axes
    BackgroundNonebackground color for the plot
    BaselinePositionAutomatichow to align with a surrounding text baseline
    BaseStyle{}base style specifications for the graphic
    ClippingStyleNonewhat to draw where curves are clipped
    ColorFunctionAutomatichow to determine the coloring of curves
    ColorFunctionScalingTruewhether to scale arguments to ColorFunction
    ContentSelectableAutomaticwhether to allow contents to be selected
    CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
    Epilog{}primitives rendered after the main plot
    EvaluationMonitorNoneexpression to evaluate at every function evaluation
    ExclusionsAutomaticpoints in x to exclude
    ExclusionsStyleNonewhat to draw at excluded points
    FillingNonefilling to insert under each curve
    FillingStyleAutomaticstyle to use for filling
    FormatTypeTraditionalFormthe default format type for text
    FrameFalsewhether to put a frame around the plot
    FrameLabelNoneframe labels
    FrameStyle{}style specifications for the frame
    FrameTicksAutomaticframe ticks
    FrameTicksStyle{}style specifications for frame ticks
    GridLinesNonegrid lines to draw
    GridLinesStyle{}style specifications for grid lines
    ImageMargins0.the margins to leave around the graphic
    ImagePaddingAllwhat extra padding to allow for labels etc.
    ImageSizeAutomaticthe absolute size at which to render the graphic
    LabelingSizeAutomaticmaximum size of callouts and labels
    LabelStyle{}style specifications for labels
    MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
    MeshNonehow many mesh points to draw on each curve
    MeshFunctions{#1&}how to determine the placement of mesh points
    MeshShadingNonehow to shade regions between mesh points
    MeshStyleAutomaticthe style for mesh points
    MethodAutomaticthe method to use for refining curves
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlightingAutomatichighlighting effect for curves
    PlotInteractivity$PlotInteractivitywhether to allow interactive elements
    PlotLabelNoneoverall label for the plot
    PlotLabelsNonelabels to use for curves
    PlotLegendsNonelegends for curves
    PlotPointsAutomaticinitial number of sample points
    PlotRange{Full,Automatic}the range of y or other values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotRegionAutomaticthe final display region to be filled
    PlotStyleAutomaticgraphics directives to specify the style for each curve
    PlotTheme$PlotThemeoverall theme for the plot
    PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
    Prolog{}primitives rendered before the main plot
    RegionFunction(True&)how to determine whether a point should be included
    RotateLabelTruewhether to rotate y labels on the frame
    ScalingFunctionsNonehow to scale individual coordinates
    TargetUnitsAutomaticunits to display in the plot
    TicksAutomaticaxes ticks
    TicksStyle{}style specifications for axes ticks
    WorkingPrecisionMachinePrecisionthe precision used in internal computations

Examples

open all close all

Basic Examples  (4)

Powers show up as straight lines on a log-log plot:

Plot several functions with legends:

Label each curve:

Fill between curves:

Scope  (30)

Sampling  (7)

More points are sampled when the function changes quickly:

The plot range is selected automatically:

Ranges where the function becomes negative are excluded:

The curve is split when there are discontinuities in the function:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Use Exclusions to remove points or split the resulting curve:

Labeling and Legending  (11)

Label curves with Labeled:

Place the labels relative to the curves:

Label curves with PlotLabels:

Place the label near the curve at an value:

Use a scaled position:

Specify the text position relative to the point:

Label curves automatically with Callout:

Place labels at specific locations:

Include legends for each curve:

Use Legended to provide a legend for a specific curve:

Use Placed to change the legend location:

Curves usually have interactive callouts showing the coordinates when you mouse over them:

Including specific wrappers or interactions, such as tooltips, turns off the interactive features:

Choose from multiple interactive highlighting effects:

Use Highlighted to emphasize specific points in a plot:

Presentation  (12)

Multiple curves are automatically colored to be distinct:

Provide explicit styling to different curves:

Add labels:

Create legends from the functions:

Specify labels for legends:

Provide an interactive Tooltip for each curve:

Create filled plots:

Use a theme with a frame, grid lines, and an automatic legend:

Use a more vibrant theme:

Create an overlay mesh:

Style the curve segments between mesh points:

Show multiple curves in a row of separate panels:

Use a column instead of a row:

Use multiple rows or columns:

Use ScalingFunctions to reverse the y axis:

Scale both x and y axes:

Options  (96)

ClippingStyle  (5)

Omit clipped regions of the plot:

Show the clipped regions like the rest of the curve:

Show clipped regions with red lines:

Show clipped regions as thick at the bottom and red at the top:

Show clipped regions as red and thick:

ColorFunction  (5)

Color by scaled coordinate and scaled coordinate, respectively:

Color a curve red when its absolute coordinate is above 1:

Fill with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use a color function that is red at powers of 10:

ColorFunctionScaling  (3)

No argument scaling on the left, automatic scaling on the right:

Scaling is done on a linear scale in the original coordinates:

Use a color function that is red at powers of 10:

EvaluationMonitor  (3)

Find the list of values sampled by LogLogPlot:

Show where LogLogPlot evaluates the function:

Count how many times the function is evaluated:

Exclusions  (2)

Use automatic methods for computing exclusions, in this case for a piecewise function:

Indicate that no exclusions should be computed:

ExclusionsStyle  (2)

Use dashed lines to indicate the vertical asymptotes:

Use blue points to highlight the exclusions:

Filling  (7)

Use symbolic or explicit values:

Overlapping fills by default combine using opacity:

Fill between curve 1 and the axis:

Fill between curves 1 and 2:

Fill between curves 1 and 2 with a specific style:

Fill between curves 1 and 2; use yellow when 1 is below 2 and green when 2 is above 1:

Fill between curves 1 and with yellow:

FillingStyle  (4)

Use different fill colors:

Fill with opacity 0.5 yellow:

Fill with red below and blue above:

Use a variable filling style obtained from a ColorFunction:

LabelingSize  (4)

Textual labels are shown at their actual sizes:

Image labels are automatically resized:

Specify a maximum size for textual labels:

Specify a maximum size for image labels:

Show image labels at their natural sizes:

MaxRecursion  (2)

The default sampling mesh:

Each level of MaxRecursion will subdivide the initial mesh into a finer mesh:

Mesh  (3)

Show the initial and final sampling meshes:

Use 20 mesh levels evenly spaced in the unscaled direction:

Use an explicit list of values for the mesh in the direction:

MeshFunctions  (4)

Use a mesh evenly spaced in the and directions:

Mesh functions use the unscaled values in the and directions:

Use Log to scale the mesh functions:

Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling the curve:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

MeshStyle  (4)

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big red mesh points in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotHighlighting  (8)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

Use Highlighted[…,None] to disable highlighting for a single curve:

Move the mouse over the curve to highlight it with a ball and label:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the curve to highlight it with a label and droplines to the axes:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Highlight the curves at a fixed value:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Use a component that shows the points on the curve closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the curve closest to the mouse cursor:

Use Callout options to change the appearance of the label:

Combine components to create a custom effect:

PlotInteractivity  (4)

Plots have interactive highlighting by default:

Turn off all the interactive elements:

Interactive elements provided as part of the input are disabled:

Allow provided interactive elements and disable automatic ones:

PlotLabel  (1)

Add an overall label to the plot:

PlotLabels  (5)

Specify text to label curves:

Place the labels above the curves:

Place the labels differently for each curve:

PlotLabels->"Expression" uses functions as curve labels:

Use callouts to identify the points:

Use None to not add a label:

PlotLayout  (2)

Place each curve in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

PlotLegends  (7)

No legends are used by default:

Create a legend based on the functions:

Create a legend with placeholder text:

Specify labels for each curve:

PlotLegends picks up PlotStyle values automatically:

Use Placed to position legends:

Place legends inside:

Use LineLegend to modify the appearance of the legend:

PlotPoints  (1)

Use more initial points to get a smoother curve:

PlotRange  (1)

Show the curve only where it is positive:

PlotStyle  (6)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with MeshShading:

MeshStyle by default uses the same style as PlotStyle:

PlotTheme  (1)

Use a theme with a frame, grid lines, and an automatic legend:

Turn off the grid lines:

RegionFunction  (2)

Show the curve where :

Exclude the region where :

ScalingFunctions  (2)

By default, both axes have a log scale:

Reverse the direction of the y axis:

Reverse the direction of both axes:

Properties & Relations  (4)

LogLogPlot samples more points where it needs to:

LogLogPlot is a special case of Plot for curves:

Use LogPlot and LogLinearPlot for logarithmic plots in the other directions:

Use ListLogPlot for data:

See Also

ListLogLogPlot  LogPlot  LogLinearPlot  Plot  ParametricPlot

Tech Notes

    ▪
  • Some Special Plots

Related Guides

    ▪
  • Function Visualization

History

Introduced in 2007 (6.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2016 (10.4) ▪ 2016 (11.0) ▪ 2018 (11.3) ▪ 2021 (13.0) ▪ 2022 (13.1) ▪ 2023 (13.3) ▪ 2025 (14.3)

Wolfram Research (2007), LogLogPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LogLogPlot.html (updated 2025).

Text

Wolfram Research (2007), LogLogPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LogLogPlot.html (updated 2025).

CMS

Wolfram Language. 2007. "LogLogPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/LogLogPlot.html.

APA

Wolfram Language. (2007). LogLogPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogLogPlot.html

BibTeX

@misc{reference.wolfram_2025_loglogplot, author="Wolfram Research", title="{LogLogPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/LogLogPlot.html}", note=[Accessed: 01-March-2026]}

BibLaTeX

@online{reference.wolfram_2025_loglogplot, organization={Wolfram Research}, title={LogLogPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/LogLogPlot.html}, note=[Accessed: 01-March-2026]}

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