logplot for negative valued function

Question

I would like to plot the following function

Plot[(1/x (0.01/(0.01 + x^2) - (10/(10 + x^2))^2)), {x, 0, 10}, 
 Frame -> True, PlotRange -> All]

which is very peaked at 0.01 in log scale, to show it up to higher values, i.e.:

LogPlot[-(1/x (0.01/(0.01 + x^2) - (10/(10 + x^2))^2)), {x, 0, 100}, 
 Frame -> True, PlotRange -> {10^-9, 10}]

However, since function is negative, I must add a minus sign to the function. I would like to get something like the log plot above, but with the y-axis going downwards and with negative values, looking similar to the plot below

LogPlot[-(1/x (0.01/(0.01 + x^2) - (10/(10 + x^2))^2))^-1, {x, 0, 10},
  Frame -> True, PlotRange -> {0.1, 10^3}]

but with the right scaling for log axis and negative value sin stead of positive ones, is it possible?

Thanks in advance

Answer 1

It seems something like this does the work. Taking the inverse, just produce the negative value for the log. Then, relabeling the ticks (but using also the inverse, solves the work)

myTicks = 
 N[Table[{10^-i, -10^i}, {i, -9, 1}]]; LogPlot[-f[x], {x, 0, 100}, 
 Frame -> True, PlotRange -> {10^-9, 10}]
LogPlot[-f[x]^-1, {x, 0, 100}, Frame -> True, 
 PlotRange -> {1/10, 10^9}, 
 FrameTicks -> {Automatic, myTicks, None, None}]

Thanks to Boson which helped here.