I have two diagrams for the same function `func1(x_,y_):= Exp(x)-y`

. One is represented in a "fake" logarithmic linear manner as:

`p1 = ContourPlot(func1(10^(x),y) == 0,{x,-3,-1},{y,0.1,10.})`

(the x-axis is "log" scale) and the graph is:

The other is drawn with the built-in one `LogLinearPlot()`

work as:

`p2 = LogLinearPlot(Exp(x), {x,10^(-3),10}, PlotRange -> {Automatic,{0.1,10}}, PlotStyle -> Green)`

and the action is:

Then I combine them with `Show(p1,p2)`

. And since I expect them to collapse, I get the following graphic (blue is instead) `p1`

and is green `p2`

):

I do not understand why the two graphics do not coincide …? I checked and the green graph is shifted (and si wrong) while the blue one is correct (at `y=10`

, `x=0.35`

(correct) for blue curve during `x=0.834`

for green).

I know that `Show()`

takes the axis scaling of the first diagram into its argument (here) `p1`

). But I thought that instead of matching scales, `Show`

she would draw with that `x,y`

Coordinates of the respective diagrams (I don't really know how `Show()`

combines diagrams with different scales, but same value ranges). Since the `x,y`

Values ββare the same in both cases (I don't know how `Show()`

would know that though), I expected them to collapse.

Alternatively with `Show(p2,p1)`

I get

Why do they cross exactly? `y=Exp(1)`

? Why the blue plot in the last picture `p1`

is not horizontal up `x=10^(-3)`

? How is it decided how the land should be combined? I feel like I'm missing something small but important here. Thanks a lot.

**EDIT 1:** At the suggestion of @kglr in the comment, I replaced `10^(x)`

to `Exp^(x)`

in the `ContourPlot`

. The blue curve has changed (the green remains the same) and now the graphics match! But I still don't really understand how `Show()`

decides to combine them and why they didn't initially coincide …? Because now both look exactly like the green curve in Figure 3 above. So now, `y=Exp(Exp(x))`

and this is true e.g. at the `y=10`

in pic3. The `x=0.834`

which does ______________ mean `y=Exp(Exp(0.834))`

that is the same `10`

. So that means `Show()`

plans `Exp(Exp(x))`

to the `p2`

held in pic3 `Exp(10^(x))`

. I find it strange. How did `Show()`

decide to do that? Thanks a lot.