I take your expression from your latest post

f = FullSimplify[176/100 + 128117/10^7 (Log[10, 65] - Re[Log[10, (309/10 - 15/10 X)]]) - 426911/10^8
   (Log[10, 369720589101871337890625 X^2]-(14 Re[Log[10, 500000001/10000000-7 X]]+Re[Log[10,41/10-5/10 X]]))]

and then

Plot[f, {X, 0, 10}, WorkingPrecision -> 20]

and then

and then in a fraction of a second

FindRoot[f == 0, {X, 7}, WorkingPrecision -> 20]

gives {X -> 7.1428571571087710129} a one warning about it likely not really being 20 digits of precision.

But I suspect those Re[] may be giving you something very different from what you are expecting to measure with an instrument in the lab.

Perhaps if you could retreat from all of the changes and little errors and revisions and patches and ways of trying to possibly make Mathematica happy, perhaps even well back before your first post here, and just explain in the simplest, clearest possible way what you are certain the original problem to solve really is then someone might be able to take a few minutes and see if they can find a way to quickly calculate a solution.

Ok, thanks, now I at least understand why it wouldn't compute. Could you give me some kind of advice on how to get

Log10[(369720589101871337890625 X^2)/((500000001/10000000 - 7 X)^14 (4.1 - 0.5 X))]    

to be either? I'm assuming to get that to be an integer is pretty unrealistic. Is there a chance to get it to be a fraction? My initial idea was rounding that, but it failed. Probably because you can't round variables...

Thank you Bill,

Yesterday evening I tried the Plot[ ], too, but sadly it didn't lead to a solution I was satisfied with...

Both, the find root and the plot give back the result 3.57[...], which was my original result. As I looked at the Formula noticed that it was using my original mistaken one and not the "revised" version.

Thanks for your effort!