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File:Logarithm inversefunctiontoexp.svg

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    Original file (SVG file, nominally 240 × 279 pixels, file size: 11 KB)

    Summary

    Description
    العربية: دالة اللغارتم باعتبارها معكوس الدالة الأسية، موضحة على نفس البيان مع "مستقيم الانعكاس" بزاوية 45 درجة.
    English: Logarithm function as the inverse of an exponential, shown on the same graph together with the 45° “mirror line”.
    Date
    Source Own work
    Author Stpasha
    Other versions Logarithm_inversefunctiontoexp.png

    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], 
     Darker[Red]}},
  AxesStyle -> 
   Directive[FontSize -> 12, FontFamily -> "Arial", 
    Thickness[0.003]],
  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, "\!\(\*
StyleBox[\"t\",\nFontSlant->\"Italic\"]\)"}}},
  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}],
    Inset[
     "\!\(\*SubscriptBox[\"log\", \"b\"]\)\!\(\*AdjustmentBox[\"(\",\n\
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
0.}}]\)\!\(\*AdjustmentBox[\"x\",\n\
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
0.}}]\)\!\(\*AdjustmentBox[\")\",\n\
BoxMargins->{{-0.12355212355212356`, 0.12355212355212356`}, {0., \
0.}}]\)", {3.7, 2.3}]
    }]
Export["Logarithm_inversefunctiontoexp.svg", g2]

    Licensing

    I, the copyright holder of this work, hereby publish it under the following license:
    Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
    The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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    inception

    4 March 2011

    File history

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    Date/TimeThumbnailDimensionsUserComment
    current02:38, 5 March 2011Thumbnail for version as of 02:38, 5 March 2011240 × 279 (11 KB)Stpasha{{Information |Description ={{en|1=Logarithm function as the inverse of an exponential, shown on the same graph together with the 45° “mirror line”. }} |Source ={{own}} |Author =Stpasha |Date =2011-03-04

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