@acer 
I have not understood every details of the explanation. It's a bit beyond my skills.
But using abs works.
So thank you.

@Carl Love Thank you very much.

@Carl Love 
I have a last question with the custom tickmarks.
I would like to print 10^-2 10^-1 10⁰ 10¹ instead of 0.01 0.1 1 10 
So I change X to [10^-2, etc , 10^1] but maple print  etc 
How can I print on the plot 10^-2 ?

@Markiyan Hirnyk 
The first picture is made with your code (with a 10,10 grid)

The second is with the code of Carl love : 

The gradution at the foot of the picture should be read : 10^x

You can see it's much more accurate on the left.
You can see the "circles" I mentionned few post upper.
Thank you for your help too

@Carl Love 
THIS IS GREAT ! That works perfectly !!!
Thank you very much !

@Markiyan Hirnyk I think, anything I can say will not convince you.
So I ask you just one question : If your solution was working, why would I say it doesn't ? Don't you think I just want some code working ?

@Markiyan Hirnyk 
Sorry, my english is not very good.
I wanted to say : The code called densityplot then display the densityplot then print on the screen the content of T as you can see in my previous post. 
I have not used densityplot with T as an argument.
My example is not very simple but I know what the result looks like. That's why I use it and I think it's clear enough.

Rendement take 2 real arguments, calculate the solution of a differential system then evaluate the solution. Then save the result and the 2 arguments in T, an array.
Then I display the densityplot 
Then I print the content of T (the form is [ [argument 1, argument 2],value of rendement])
Thus, we can see how densityplot have called rendement.
If you look at the content of T (just a few message upper), you can see the first argument takes the values : 0.01, 2.5, 5, 7.5 and 10
That shows densityplot calculate with a linear grid (spacing of 2.5) and not a logarithmic grid.
If the grid used to calculate have been logarithmic the first argument should have taken some values like : 0.01, 0.1,1 and 10.

I think that base my statement.
I have no interest to lie to you. I want my code to work ...
I hope you understant better what I wanted to explain.

@Markiyan Hirnyk 
Sorry, when I answered, there was another message. You have probably edited your message.
But, now I don't understand what you want to say with this new message. What's the meaning of the error ? 

@Markiyan Hirnyk 
Yes, I have used a [5,5] grid to quickly make the plot.
When you use a [10,10] grid it looks better.
But that's not my point, because the way the plot is calculated is still the same, the rectangles are juste smaller.
I would like to adapt the size of the rectangles otherwise i'll have to run my computer for weeks if I want enough accuraty between 0.01 and 0.1.
If it was calculated with what i called a logarithmic scale, you would see something like "circles" around the red spot in the middle. But we can see the "circles" are not closed on the left of the picture because the rectangles have not the adapted size.

@Markiyan Hirnyk 
rendement take 2 real arguments, calculate something (but what it calculates is not the point here) then save in the array called T the 2 arguments and the value of rendement.
The code called densityplot then display T. Thus we could see how maple calculate the density plot.
If you look at the values of T you see, its firt 0.01 then 2.5 then 5 then 7.5 then 10
That shows even if there is the option "axis[1]=[mode=log]", when maple calculate the density plot, the grid used is linear (with a steady stepsize of 2.5) and not logarithmic otherwise the value would have been something like : 0.01, 0.05, 0.1, 0.5,1 etc 

Download tentative5.mw

Download tentative5.mw

@Markiyan Hirnyk 
Yes I'm. 
I'm sorry, I don't know why the picture don't work.
This is my file where the array is displayed

@Markiyan Hirnyk 
I try : 

Rendement is a procedure which take 2 reals then  return a number and save the pair of reals and the value of rendement in a array. 
I have displayed the array : 

The first parameter increase by 2.5 with a linear scale
Not a logarithmic scale.

@Markiyan Hirnyk 
It's still the same problem.
This code does not modify how the density plot is calculated. The grid used to calculate is still linear.
But the grid showed is logarithmic. 

@Markiyan Hirnyk 
The picture is good but only the picture not the plot.
The option "grid=[n,m]" not only controls the display of a n by m grid on the densityplot, it controls how the densityplot is calculated (a value is calculated for each rectangle).
I would like to change how the densityplot is calculated with a logarithmic scale.
Thus, there will be as many rectangles calculated from 0.1 to 1 than from 1 to 10. 
I hope it's more understandable.
And again, thank you for your help.

@Markiyan Hirnyk 
Thank you for your answer.
This is what I don't want. 
On the picture, the rectangles are very wide from 10^-3 to 10^-1 then very narrow (because they have a regular spacing when they are calculated). So the plot is not very accurate. 
I would like to make what I called a logarithmic spacing of the rectangles, thus they will appear regularly spaced on the picture. 
I hope it's clearer
PS : I apologise, it's a bit difficult for me to explain what I want to do because english is not my native language.