Checked content

File:Logarithm inversefunctiontoexp.svg


English: Logarithm function as the inverse of an exponential, shown on the same graph together with the 45° “mirror line”.
Date 4 March 2011
Source Own work
Author Stpasha

Source code in Mathematica

t = 3;
g2 = Plot[{Log[2, x], 2^x}, {x, -3, 5}, 
  PlotRange -> {{-2, 4.5}, {-3, 5}}, AspectRatio -> 8/6.5, 
  ImageSize -> 240,
  PlotStyle -> {{Thickness[0.007], Blue}, {Thickness[0.007], 
  AxesStyle -> 
   Directive[FontSize -> 12, FontFamily -> "Arial", 
  AxesLabel -> {"x", None},
  Ticks -> {{{Log[2, t], "\!\(\*SubscriptBox[\"log\", \"b\"]\)(\!\(\*
StyleBox[\"t\",\nFontSlant->\"Italic\"]\))"}, {t, "\!\(\*
StyleBox[\"t\",\nFontSlant->\"Italic\"]\)"}}, {{Log[2, t], 
      "\!\(\*SubscriptBox[\"log\", \"b\"]\)(\!\(\*
StyleBox[\"t\",\nFontSlant->\"Italic\"]\))"}, {t, "\!\(\*
  Epilog -> {
    Line[{{-2.3, -2.3}, {3.5, 3.5}}],
    Line[{{t, Log[2, t]}, {Log[2, t], t}}],
    Dotted, Gray,
    Line[{{Log[2, t], 0}, {Log[2, t], 5}}],
    Line[{{t, 0}, {t, Log[2, t]}}],
    Line[{{0, Log[2, t]}, {4, Log[2, t]}}],
    Line[{{0, t}, {Log[2, t], t}}],
    Black, PointSize[Medium],
    Point[{{t, Log[2, t]}, {Log[2, t], t}}],
    FontSize -> 12, FontFamily -> "Arial",
    Inset["\!\(\*SuperscriptBox[\"b\", \"x\"]\)", {2.5, 4.2}],
     "\!\(\*SubscriptBox[\"log\", \"b\"]\)\!\(\*AdjustmentBox[\"(\",\n\
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
0.}}]\)", {3.7, 2.3}]
Export["Logarithm_inversefunctiontoexp.svg", g2]


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