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, after doing some try and error I tried to find out what the problem was rationally. It became pretty obvious that Solve[ ] has a problem with sums of multiple logarithms in the form of aLog[b-cx]. As I had noticed that in my plot I always got some kind of complex part I tried expanding all the logarithms (by hand, not too difficult) and placing a Re[ ] in front of every logarithm of that form. Wolfram Alpha refused to compute that (runtime again), so I tried it on my laptop, and I didn't run into my usual "inexact coefficients" error, Yay!
Well, my computer is calculating for hours now (app. 50% (workload/usage) at 2.6 GHz). This reminds me that my theoretical chemistry lecturer liked to say (paraphrased):

> Exponential functions are a bitch to calculate. That's why we approximate them with the Taylor-Series.

Well, that's what I'm going to try next. Here's the function I'm using right now:

NSolve/Solve/Reduce[0 == 
  1.76 + 0.0128117 (Log[10, 65] - Re[Log[10, (30.9 - 1.5 X)] ]) - 
   0.00426911 
    ( Log[10, 369720589101871337890625 X^2] - (14 Re[ Log[10, 500000001/10000000 - 7 X] ] + Re[ Log[10, 4.1 - 0.5 X] ] )
        ), X]

Could anyone tell me if I can simply cut off the imaginary part? As I want a rational (real) solution, I'd assume so. Or does this change the result I'll get (significantly)?
I'll also insert Marco's WorkingPrecision in the Taylor-Series approach.

Edit:
Ok, I did that. It lead me to a solution, but not a good one. The term that is making problems is:

Log[50-7X]

That simply makes this equasion unsolvable in $/R$. This led me back to my beginning, And I see the problem, it's my formula again. Right now I don't really know how to solve it, so I can't put it into Mathematica. I'll have to rethink. Thank you all for your help, I think I learnd something while trying to get this calculation to work.

Have a nice day!
J

Thank you Marco!

The working Precision I will try, and the Rationalize ] function seems interesting, too.
The problem is, that you used my first 'mistaken' function, not the 'revised' one. If I correct my error and try your formula on the cloud I get terminated because of computing time. (Sometimes it's the Wolfram Engine that's been [terminated, too. ;) - I assume that the run time extension doesn't work here neither, because it said something about buying a new plan.

I just tried my "latest" attempt on the cloud (which is nice, tank you for that, too. I didn't know about that), which produced a "The Wolfram Engine has been terminated because the evaluation time limit was reached" message, too.

Some things in your formula I don't understand (and don't find anything in the Mathematica built in help about), so if you could elaborate, that'd be great.

• What does sols= or /. sols do?
• Why do you rationalize the coefficients? They should not be the problem, I'd assume that the logarithms are. 0.059 is rational either way, isn't it?
• The two numerical zeros (which I got when I tried what you did), what do they mean? I assume that the two solutions are not the same, but numerically not distinguishable, or did I get that wrong? - That mean the sols would have something to do with that.

Thank you again for your time!

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!