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I'm having difficulty understanding how to express text in Epilog that is dynamically updated using Log[b, x]. Mathematica changes this to base $e$, but I would like it to be Log[b, x] in traditional format with base $b$, and I can't seem to make it work. I'm guessing I need to break the $\log$ apart using boxes or something, but don't know how to make a subscript that is a dynamically updated b value. Any ideas?

Manipulate[
 Plot[{b^x, x, Log[b, x]}, {x, -10, 10}, 
  PlotRange -> {{-5, 5}, {-10, 10}}, PerformanceGoal -> "Quality", 
  ImageSize -> All, 
  Epilog -> {Text[b^x, {-3, 4}], Text[Log[b, x], {3, -5}]}, 
  GridLines -> {Range[-10, 10, 1], Range[-10, 10, 1]}, 
  GridLinesStyle -> Opacity[.04]], {{b, 2, "Choose a base"}, 0.01, 4}]
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    $\begingroup$ Epilog -> {Text[Subscript[Log, b] "(x)", {3, -5}]}] $\endgroup$ – Dr. belisarius Jan 16 '16 at 6:48
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The code in the OP will work right off the bat if the following (sadly undocumented) setting is first executed:

SetSystemOptions["SimplificationOptions" ->
                 {"AutosimplifyTwoArgumentLog" -> False}]

After running that line, the Manipulate[] works as expected:

now it works!

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Here's a way that let's Mathematica take care of the typesetting. Use With to inject the value of b into a held expression for the logarithm (see HoldForm).

Epilog -> {Text[b^x, {-3, 4}], Text[With[{b = b}, HoldForm@Log[b, x]], {3, -5}]}

Mathematica graphics

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Thanks to Dr. Belisarius,

Epilog -> {Text[Subscript[Log, b] "(x)", {3, -5}]}]
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    $\begingroup$ I think this Text[Row[{Subscript[Log, b], "(x)"}], {3, -5}] is preferrable. $\endgroup$ – Mike Honeychurch Jan 16 '16 at 22:41

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