       RE: LogPlot != Plot[Log]

• To: mathgroup at smc.vnet.net
• Subject: [mg24281] RE: [mg24266] LogPlot != Plot[Log]
• From: Wolf Hartmut <hwolf at debis.com>
• Date: Fri, 7 Jul 2000 00:11:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> -----Original Message-----
To: mathgroup at smc.vnet.net
> Sent:	Thursday, July 06, 2000 5:11 AM
> To:	mathgroup at smc.vnet.net
> Subject:	[mg24266] LogPlot != Plot[Log]
>
> Dear Steve Christensen,
>
> I should like to post the following question to the Mathgroup. I am
> relatively new with Mathematica and I encountered a problem..
>
>
> Dear MathGroup,
> I should like to demonstrate some transformation rules graphically using
> Mathematica extended capabilities. However, the simplest example failed:
> Let assume a simple exponential function with real parameters:
>
> C1[t_] := C0*Exp[-kel*t]
>
> param = {C0 -> 100, kel -> 1}
>
> we can plot the function easily:
>
> g1 = Plot[C1[t] /. param, {t, 0, 2}, PlotRange -> {{0, 2}, {10, 100}}]
>
>
> We can also make a half- logarithmic plot:
>
> g2 = Plot[Log[E, C1[t]] /. param, {t, 0, 2}, PlotStyle -> {RGBColor[0, 0,
> 1],
> Dashing[{0.05, 0.05}]},  PlotRange -> {{0, 2}, {Log, Log}}]
>
> In addition we can convert the y-axis to a logarithmic one:
>
> g3 = Show[g2, Ticks -> Join[{FullOptions[g2, Ticks][], FullOptions[g2,
> Ticks][] /. {x_, y_Real, len_, style_} :> {x, Exp[y], len, style}}]]
>
> We can obtain a half-logarithmic plot by using the LogPlot function:
>
> << Graphics`Graphics`
>
> g4 = LogPlot[C1[t] /. param, {t, 0, 2}, PlotRange -> {{0, 2}, {10, 100}}]
>
> Now I would expect that plot g4 and g3 become identic:
>
> Show[{g3, g4}, PlotRange -> All]
>
> But it is not the case. I am sure that there is something wrong. Any help
> would be appreciated.
> With best regards
>
>
[Wolf Hartmut]

There is no mystery here, you only need base 10 for the logarithm. See

In:=
g2a = Plot[Log[10, C1[t]] /. param, {t, 0, 2},
PlotStyle -> {RGBColor[1, 0, 1], Dashing[{0.05, 0.07}],
Thickness[0.01]},
PlotRange -> {{0, 2}, {Log[10, 10], Log[10, 100]}}]

In:=
g3a = Show[g2a,
Ticks -> Join[{FullOptions[g2a, Ticks][],
FullOptions[g2a, Ticks][] /. {x_, y_Real, len_, style_} :> {x,
10^y, len, style}}]]

and then

In:= Show[{g4, g3a}]

However

In:= g3d = Show[g2a, Ticks -> {Automatic, LogScale[1, 2]}]

In:= Show[{g3d, g4}]

is less work!

Kind regards,
Hartmut Wolf

```

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