LogLinearPlot

LogLinearPlot[f,{x,x_min,x_max}]

generates a log-linear plot of f as a function of x from x_min to x_max.

LogLinearPlot[{f₁,f₂,…},{x,x_min,x_max}]

plots several functions f_i.

LogLinearPlot[{…,w[f_i],…},…]

plots f_i with features defined by the symbolic wrapper w.

LogLinearPlot[…,{x}∈reg]

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

Details and Options

LogLinearPlot effectively generates a curve in which f is plotted against Log[x], but with tick marks indicating the original values of x.
LogLinearPlot makes logarithmic functions appear as straight lines.
LogLinearPlot evaluates f at different values of x to create a smooth curve of the form {x,f[x]}.
Gaps are left at any x where the f_i evaluate to anything other than 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.

LogLinearPlot treats the variable x as local, effectively using Block.
LogLinearPlot 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[{f₁,…}] wrap a collection of f_i

w₁[w₂[…]] 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

LogLinearPlot 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
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
PlotLabel	None	overall label for the plot
PlotLabels	None	labels to use for curves
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
With the default settings Exclusions->Automatic and ExclusionsStyle->None, LogLinearPlot 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 f_i as the legend text.
LogLinearPlot 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 LogLinearPlot 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.