How to define range for Manipulate using exponents

Question

I have a function:

f[x_,y_] = x*y // ScientificForm;
Manipulate[f[x,y], {x, 10^-1, 10^-10}, {y, 0.01, 1, 0.01}]

When I try to execute it - it does work. However I want my x to increment in following manner: for x, 10^-1, 10^-2, 10^-3, ..., 10^-10 and for y, 0.01, 0.02, ..., 0.1, ..., 0.11, ..., till eventually 1;

I can't get my head around this. Could somebody please share any links on how to actually build interface in Mathematica. That would be very much appreciated

Answer 1

Using the logManipulator from my answer to Logarithmic slider, you can also achieve your objective via

Manipulate[
 f[x, y],
 {x, 10.^-10, 10^-1, 10, logManipulator[##] &},
 {y, 0.01, 1, 0.01}]

---

Code for logManipulator:

ClearAll[logManipulator];
With[{smallerRule = {Large -> Medium, Medium -> Small, Small -> Tiny}},
 logManipulator[Dynamic[x_], range_: {1, 10}, 
   OptionsPattern[Manipulator]] := With[{
    logrange = Log10[range],
    imagesize = OptionValue[ImageSize] /. Automatic -> Medium,
    inputfieldsize = 
     OptionValue[ImageSize] /. Automatic -> Medium /. smallerRule,
    enabled = OptionValue[Enabled],
    continuousaction = OptionValue[ContinuousAction],
    appearance = 
     First[Cases[OptionValue[Appearance], 
        Tiny | Small | Medium | Large] /. {} -> {Automatic}],
    labeled = ! FreeQ[OptionValue[Appearance], "Labeled"] || ! 
       FreeQ[OptionValue[AppearanceElements], "InlineInputField"],
    opener = 
     OptionValue[AppearanceElements] /. {Automatic -> True, 
       All -> True, None -> False, 
       l_List :> (Cases[l, Except["InlineInputField"]] =!= {})},
    inputfield = 
     MatchQ[OptionValue[AppearanceElements], Automatic | All] ||
      ! FreeQ[OptionValue[AppearanceElements], "InputField"],
    appearanceelements = 
     OptionValue[AppearanceElements] /. {Automatic -> All, None -> {},
        l_List :> Cases[l, Except["InlineInputField" | "InputField"]]},
    autoaction = OptionValue[AutoAction],
    exclusions = OptionValue[Exclusions]},
   ReleaseHold@MakeExpression[
     PaneBox[
      DynamicModuleBox[{
        Typeset`open$$ = ! FreeQ[OptionValue[Appearance], "Open"],
        Typeset`paused$$ = OptionValue[PausedTime],
        Typeset`rate$$ = OptionValue[AnimationRate],
        Typeset`dir$$ = OptionValue[AnimationDirection]},
       StyleBox[
        DynamicBox[
         FEPrivate`FrontEndResource["FEExpressions", "Manipulator04"][
          Dynamic[x],
          Dynamic[Log10[x], (x = 10^#) & ],
          logrange,
          imagesize,
          inputfieldsize,
          enabled,
          continuousaction,
          appearance,
          labeled,
          opener,
          inputfield,
          appearanceelements ,
          autoaction,
          exclusions,
          Dynamic[Typeset`open$$],
          Dynamic[Typeset`paused$$],
          Dynamic[Typeset`rate$$],
          Dynamic[Typeset`dir$$]]],
        DynamicUpdating -> True],
       DynamicModuleValues :> {}],
      BaselinePosition -> (OptionValue[BaselinePosition] /. Automatic -> Baseline),
      ImageMargins -> OptionValue[ImageMargins]],
     StandardForm]]
 ]

Answer 2

f[x_, y_] = x*y;

Manipulate[
 f[x, y] // ScientificForm,
 {{x, 10.^-6}, 10.^Range[-1, -10, -1]},
 {{y, .5}, 0.01, 1, 0.01, Appearance -> "Labeled"}]