Scale ticks of a LogLinear Plot

Question

I have LogLinear plots for which I want to scale the ticks on the x-axis. The following MWE, which works for the linear plot is showing ticks at the wrong positions for the LogLinear plot

Clear[plot];

plot = LogLinearPlot[Erf[x], {x, 1, 100}]
scalefact= 10^(-10);
newticks = {#, scalefact #} & /@ Range[1, 100];
Show[plot, Ticks -> {newticks, Automatic}]

Since I already have the plots I would not like to scale the x-axis, I just want to change the tick specifications. Thanks.

Answer 1

You can take x-Ticks from plot either with:

oldticks = Charting`ScaledTicks[{Log, Exp}][Log@1, Log@100, {6,6}]

or with:

oldticks = (Ticks /. AbsoluteOptions[plot, Ticks])[[1]]

Now change labels:

Show[plot, 
 Ticks -> {oldticks /. {a_?NumericQ, b_?NumericQ, c__} :> {a, scalefact b, c}, 
  Automatic}]

EDIT

To answer new request in comment about having only specific ticks:

newTicks = {Log[#], scalefact #} & /@ {1., 10., 100.}
newTicksEmpty = {Log[#], Spacer[0]} & /@ {1., 10., 100.}
Show[plot, 
 FrameTicks -> {{Automatic, Automatic}, {newTicks, newTicksEmpty}}, 
  Frame -> True]

Minor ticks can be added with Subdivide of the corresponding interval and using technique as for newTicksEmpty:

minor = {Log@#, Spacer[0], {0.005, 0}} & /@ 
 Join[Subdivide[1, 10., 9], Subdivide[10, 100., 9]]

Show[plot, 
 FrameTicks -> {{Automatic, Automatic}, {Join[newTicks, minor], 
    Join[newTicksEmpty, minor]}}, Frame -> True]

Answer 2

Try this:

newticks = Map[{#, # *1.*10^-10} &, Range[1, 100]];

which only differs from your definition by a factor 1..

Have fun!