<< Graphics`Arrow`
<< Graphics`Legend`

    
$TextStyle = {FontFamily -> "Courier", 
          FontSize -> 14};
gridstyle = {{{-1, {Dashing[{0.01}], 
                Thickness[0.0025]}}, {1, {Dashing[{0.01}], 
                Thickness[0.0025]}}}, {{1, {Dashing[{0.01}], 
                Thickness[0.0025]}}, {-1, {Dashing[{0.01}], 
                Thickness[0.0025]}}}};

    
SetOptions[Plot, 
        PlotStyle -> {{RGBColor[0, 0, 0], 
              Thickness[0.005]}, {RGBColor[1, 0, 0], 
              Thickness[0.005]}, {RGBColor[0, 0, 1], 
              Thickness[0.005]}, {RGBColor[0, 1, 1], Dashing[{0.01}], 
              Thickness[0.005]}, {RGBColor[1, 0, 1], Dashing[{0.01}], 
              Thickness[0.005]}}, PlotRange -> {{xmin, xmax}, All}, 
        Frame -> True, AspectRatio -> 1/GoldenRatio, 
        TextStyle -> $TextStyle, 
        GridLines -> gridstyle];

    
xmin = -2;  xmax = 2;
f1[x_, a_] := x^a

    
g1 = 
        Plot[{f1[x, 2], f1[x, 4], f1[x, 8]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {0, 2}}, 
          DisplayFunction -> Identity, 
          FrameTicks -> {{0, 1, -1}, {0, 
                1}}, 
PlotLegend -> {"x^2", "x^4\
", "x^8"}, LegendPosition -> {-0.3,  .15}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, - .02}, 
          LegendSize -> { .7,  .2}, 
          Background -> GrayLevel[1]];

    
Show[g1, 
        DisplayFunction -> $DisplayFunction];

\(\(g2 = 
        Plot[{f1[x, 3], f1[x, 5], f1[x, 9]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {\(-3\), 3}}, 
          DisplayFunction -> Identity, GridLines -> gridstyle, 
          FrameTicks -> {{0, 1, \(-1\)}, {0, 
                1, \(-1\)}}, 
PlotLegend -> {"x^3", "x^5", "x^7"}, LegendPosition -> {\(-0.3\),  .29}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> { .7,  .2}, 
          Background -> 
            GrayLevel[1]];\)

\)
Show[g2, 
        DisplayFunction -> $DisplayFunction];

xmin = -5;  xmax = 5;
f1[x_, a_] := x^a

    
\(\(\(g0 = 
        Plot[{f1[x, \(-2\)], f1[x, \(-4\)], f1[x, \(-6\)]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {0, 10}}, 
          DisplayFunction -> Identity, GridLines -> gridstyle, 
          FrameTicks -> {{0, 1}, {0, 
                1}}, 
PlotLegend -> {"x^(-2)", "x^(-4)", "x^(-6)"}, LegendPosition -> {\(- .8\),  .15}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> { .7,  .2}, 
          Background -> GrayLevel[1]];\)\(
\)
    \)\)
Show[g0, DisplayFunction -> $DisplayFunction];

xmin = -2;  xmax = 2;
f1[x_, a_] := x^a
\(\(g3 = 
        Plot[{f1[x, \(-3\)], f1[x, \(-5\)], f1[x, \(-7\)]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {\(-2\), 2}}, 
          DisplayFunction -> Identity, GridLines -> gridstyle, 
          FrameTicks -> {{0, 1}, {0, 
                1}}, 
PlotLegend -> {"x^(-3)", "x^(-5)", "x^(-7)"\ }, LegendPosition -> {0, \(- .3\)}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> { .7,  .2}, 
          Background -> 
            GrayLevel[1]];\)

\)
Show[g3, 
        DisplayFunction -> $DisplayFunction];

xmin = 0;  xmax = 4;
f1[x_, a_] := x^(1/a)
\(\(g3 = 
        Plot[{f1[x, 2], f1[x, 4], f1[x, 8]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {0, 3}}, 
          DisplayFunction -> Identity, GridLines -> gridstyle, 
          FrameTicks -> {{0, 1}, {0, 
                1}}, 
PlotLegend -> {"x^(1/2)", "x^(1/4)", "x^(1/8)"}, LegendPosition -> {\(-0.3\),  .29}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> { .7,  .2}, 
          Background -> 
            GrayLevel[1]];\)

\)
Show[g3, 
        DisplayFunction -> $DisplayFunction];

xmin = -6;  xmax = 2;
f1[x_, a_] := a^x

    
e1 = 
        Plot[{f1[x, 2], f1[x, E], f1[x, 10]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {0, 4}}, 
          DisplayFunction -> Identity, 
          GridLines -> 
            gridstyle, 
FrameTicks -> {{1, 
                2, -1, -2, 0}, {0, 1, 2, 3, 
                4}}, 
PlotLegend -> {"2^x", "E^x\
", "10^x"}, LegendPosition -> {-0.8,  .15}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, - .02}, 
          LegendSize -> { .7,  .2}, 
          Background -> GrayLevel[1]];

    
Show[e1, 
        DisplayFunction -> $DisplayFunction];

xmin = -2;  xmax = 6;
f1[x_, a_] := (1/a)^x

    
\(\(\(e2 = 
        Plot[{f1[x, 2], f1[x, E], f1[x, 10]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {0, 4}}, 
          DisplayFunction -> Identity, 
          GridLines -> 
            gridstyle, 
FrameTicks -> {{1, 2, 3, 4, 
                5, \(-1\), \(-2\), 0}, {0, 1, 2, 3, 
                4}}, 
PlotLegend -> {"2^(-x)", "E^(-x)", "10^(-x)"}, LegendPosition -> {0,  .15}, 
          LegendTextSpace ->  .5, LegendLabel -> "", 
          LegendLabelSpace ->  .5, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> { .7,  .2}, 
          Background -> GrayLevel[1]];\)\(
\)
    \)\)
Show[e2, 
        DisplayFunction -> $DisplayFunction];

N[E]

xmin = 0;  xmax = 6;
f1[x_, a_] := Log[a, x]

    
e2 = 
        Plot[{f1[x, 2], f1[x, E], f1[x, 10]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {-4, 4}}, 
          DisplayFunction -> Identity, 
          GridLines -> 
            gridstyle, 
FrameTicks -> {{1, 2, 3, 4, 
                5, -1, -2, 0}, {-3, -2, -1, 0, 1, 2, 3, 
                4}}, 
PlotLegend -> {"log_2(x)", "\
log_E(x)", "log_10(x)"}, 
          LegendPosition -> {- .5, - .35}, 
          LegendTextSpace -> 1.2, LegendLabel -> "", 
          LegendLabelSpace ->  .8, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, - .02}, 
          LegendSize -> {1.3,  .2}, 
          Background -> 
            GrayLevel[1]];

Show[e2, 
        DisplayFunction -> $DisplayFunction];

xmin = 0;  xmax = 6;
f1[x_, a_] := Log[a, x]

    
\(\(e2 = 
        Plot[{f1[x, 1/2], f1[x, 1/E], f1[x, 1/10]}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {\(-4\), 4}}, 
          DisplayFunction -> Identity, 
          GridLines -> 
            gridstyle, 
FrameTicks -> {{1, 2, 3, 4, 
                5, \(-1\), \(-2\), 0}, {\(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
                4}}, 
PlotLegend -> {"log_(1/2)(x)", "log_(1/E)(x)", "log_(1/10)(x)"}, 
          LegendPosition -> {\(- .5\),  .25}, 
          LegendTextSpace -> 1.3, LegendLabel -> "", 
          LegendLabelSpace -> 1.2, Frame -> True, 
          LegendOrientation -> Horizontal, 
          LegendBackground -> GrayLevel[ .85], 
          LegendShadow -> { .02, \(- .02\)}, 
          LegendSize -> {1.5,  .2}, 
          Background -> GrayLevel[1]];\)
\)
Show[e2, DisplayFunction -> $DisplayFunction];

xmin = -6;  xmax = 6;
f1[x_, a_] := Log[a, x]
f2[x_, a_] := a^x
Off[Plot::"plnr"]
f12 = 
        Plot[{f1[x, 2], f2[x, 2], x}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {-5, 5}}, 
          DisplayFunction -> Identity, 
          GridLines -> {{0, 1}, {0, 
                1}}, 
FrameTicks -> {{1, 2, 3, 
                4, -1, -2, -3, -4, -5, 5, -3, 
                0}, {-3, -2, -1, 0, 1, 2, 3, 
                4, -4}}];

    
Show[f12, DisplayFunction -> $DisplayFunction];

xmin = -6;  xmax = 6;
f1[x_, a_] := Log[a, x]
f2[x_, a_] := a^x
Off[Plot::"plnr"]
f12 = 
        Plot[{f1[x, 1/2], f2[x, 1/2], x}, {x, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {-5, 5}}, 
          DisplayFunction -> Identity, 
          GridLines -> {{0, 1}, {0, 
                1}}, 
FrameTicks -> {{1, 2, 3, 
                4, -1, -2, -3, -4, -5, 5, -3, 
                0}, {-3, -2, -1, 0, 1, 2, 3, 
                4, -4}}];

    
Show[f12, DisplayFunction -> $DisplayFunction];

1/Log[10] // N