# Scales in this Logarithmic plot

I have this graph

Which is f[a] with a range {a,0.0001,1} and an arbitrary initial condition f[0.0001]==1]

I want to transform this plot into LogLogPlot and show in the new log plot the gridlines, espically the first one at ~ 0.0024 which is not clear on the current plot scale.

So what I did is changing the range of a , such that {Log[a], Log[0.0001],Log$$[1]$$}, or LogLogPlot with  {a,-9,0} , but this gives errors : Limiting value $I \pi$ + Log[9]……

Any help to reproduce an appropriate LogLogPlot covers all the range of a.

• Please post the Mathematica code,not only the picture. Jun 10, 2022 at 10:26

Keep the GridLines unchanged:
Plot[  7  10^6 Exp[-a 5], {a, 0, 1}, GridLines ->{{.0024, .6}, None}]

LogLogPlot[   7  10^6  Exp[-a 5], {a, 0, 1},GridLines -> {{.0024, .6}, None}]

• Thanks for the answer. But let me get the scales on the Log a axis. Now the grid line at 0.6 becomes at 0.51, to get the value of a, as I know in the natural logarithmic plot, I take Exp[0.51] which is 1.665 not 0.6! Jun 10, 2022 at 15:11
• Isn't Log[.6]==-.51 negative? Jun 12, 2022 at 15:14