LogPlot
LogPlot[f,{x,x_{min},x_{max}}]
generates a log plot of f as a function of x from x_{min} to x_{max}.
LogPlot[{f_{1},f_{2},…},{x,x_{min},x_{max}}]
plots several functions f_{i}.
LogPlot[{…,w[f_{i}],…},…]
plots f_{i} with features defined by the symbolic wrapper w.
LogPlot[…,{x}∈reg]
takes the variable x to be in the geometric region reg.
Details and Options
 LogPlot is also known as semilogarithmic or semilog plot, since it has one linear axis and one logarithmic axis.
 LogPlot makes exponentials appear as straight lines. It allows very small and very large values to be seen at the same time.
 LogPlot effectively generates a curve based on Log[f], but with tick marks indicating the values of the underlying function f. It visualizes the set .
 Gaps are left at any x where the f_{i} evaluate to anything other than positive real numbers or
Quantity.  The limits x_{min} and x_{max} can be real numbers or Quantity expressions.
 The region reg can be any RegionQ object in 1D.
 LogPlot treats the variable x as local, effectively using Block.
 LogPlot 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 f_{i}:

Annotation[f_{i},label] provide an annotation for the f_{i} Button[f_{i},action] evaluate action when the curve for f_{i} is clicked Callout[f_{i},label] label the function with a callout Callout[f_{i},label,pos] place the callout at relative position pos EventHandler[f_{i},events] define a general event handler for f_{i} Hyperlink[f_{i},uri] make the function a hyperlink Labeled[f_{i},label] label the function Labeled[f_{i},label,pos] place the label at relative position pos Legended[f_{i},label] identify the function in a legend PopupWindow[f_{i},cont] attach a popup window to the function StatusArea[f_{i},label] display in the status area on mouseover Style[f_{i},styles] show the function using the specified styles Tooltip[f_{i},label] attach a tooltip to the function Tooltip[f_{i}] use functions as tooltips  Wrappers w can be applied at multiple levels:

w[f_{i}] wrap the f_{i} w[{f_{1},…}] wrap a collection of f_{i} w_{1}[w_{2}[…]] use nested wrappers  Callout, Labeled, and Placed can use the following positions pos:

Automatic automatically placed labels Above, Below, Before, After positions around the curve x near 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  LogPlot has the same options as Graphics, with the following additions and changes:

AspectRatio 1/GoldenRatio ratio of height to width Axes True whether to draw axes ClippingStyle None what to draw where curves are clipped » ColorFunction Automatic how to determine the coloring of curves ColorFunctionScaling True whether to scale arguments to ColorFunction PlotLabel None overall label for the plot PlotLabels None labels to use for curves EvaluationMonitor None expression to evaluate at every function evaluation Exclusions Automatic points in x to exclude ExclusionsStyle None what to draw at excluded points Filling None filling to insert under each curve FillingStyle Automatic style to use for filling LabelingSize Automatic maximum size of callouts and labels MaxRecursion Automatic the maximum number of recursive subdivisions allowed Mesh None how many mesh points to draw on each curve MeshFunctions {#1&} how to determine the placement of mesh points MeshShading None how to shade regions between mesh points MeshStyle Automatic the style for mesh points Method Automatic the method to use for refining curves PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends for curves PlotPoints Automatic initial number of sample points PlotRange {Full,Automatic} the range of y or other values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to specify the style for each curve PlotTheme $PlotTheme overall theme for the plot RegionFunction (True&) how to determine whether a point should be included TargetUnits Automatic units to display in the plot WorkingPrecision MachinePrecision the precision used in internal computations  Possible settings for ClippingStyle are:

Automatic use a dotted line for the clipped portion None omit the clipped portion of the curve style use 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, LogPlot breaks curves at discontinuities and singularities it detects. Exclusions>None joins across discontinuities and singularities.
 Exclusions>{x_{1},x_{2},…} is equivalent to Exclusions>{x==x_{1},x==x_{2},…}.
 PlotLegends>"Expressions" uses the f_{i} as the legend text.
 LogPlot 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 LogPlot 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.
Examples
open allclose allBasic Examples (4)
Scope (25)
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 Exclusions>None to draw a connected curve:
Use PlotPoints and MaxRecursion to control adaptive sampling:
Use PlotRange to focus in on areas of interest:
Labeling and Legending (8)
Label curves with Labeled:
Place the labels relative to the curves:
Label curves with PlotLabels:
Place the label near the curve at an value:
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:
Presentation (10)
Multiple curves are automatically colored to be distinct:
Provide explicit styling to different curves:
Create legends from the functions:
Provide an interactive Tooltip for each curve:
Style the curve segments between mesh points:
Show multiple curves in a row of separate panels:
Options (81)
ClippingStyle (4)
ColorFunction (6)
Color by scaled coordinate and scaled coordinate, respectively:
Color with a named color scheme:
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:
ColorFunctionScaling (3)
EvaluationMonitor (3)
Exclusions (2)
ExclusionsStyle (2)
Filling (7)
FillingStyle (3)
LabelingSize (4)
MaxRecursion (2)
Each level of MaxRecursion will subdivide the initial mesh into a finer mesh:
Mesh (3)
MeshFunctions (4)
Use a mesh evenly spaced in the and directions:
Mesh functions use the unscaled values in the direction:
Use Log to scale the mesh functions in the direction:
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)
PerformanceGoal (2)
PlotLabels (5)
Place the labels above the curves:
Place the labels differently for each curve:
PlotLabels>"Expressions" uses functions as curve labels:
Use callouts to identify the curves:
Use None to not add a label:
PlotLegends (7)
No legends are used by default:
Create a legend based on the functions:
Create a legend with placeholder text:
Create a legend with specific labels:
PlotLegends picks up PlotStyle values automatically:
Use Placed to position legends:
Use LineLegend to modify the appearance of the legend:
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:
PlotTheme (2)
Applications (3)
Properties & Relations (4)
LogPlot samples more points where it needs to:
LogPlot is a special case of Plot for curves:
Use LogLinearPlot and LogLogPlot for logarithmic plots in the direction:
Use ListLogPlot for data:
Text
Wolfram Research (2007), LogPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LogPlot.html (updated 13).
CMS
Wolfram Language. 2007. "LogPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 13. https://reference.wolfram.com/language/ref/LogPlot.html.
APA
Wolfram Language. (2007). LogPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogPlot.html