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Complicated exponential equation

I have an equation:

e(17−t)/10−4e(26−t)/40=xe^{(17-t)/10}-4e^{(26-t)/40} = x

Where x is a known number (it's actually the sum of 6 different exponents of e)

How can I get t? I suspect I'm having a thick moment, and if worst comes to worst I'll just stick it into mathematica, but I'd like to solve it properly.

Thanks in advance for any suggestions
change it into logs and see what happens
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Avatar for DFranklin
DFranklin
18
It has an analytic solution, but it's going to be horrible.

If you set y = e^{-t/40}, then you have

e1.7y4−4e0.65y=xe^{1.7}y^4 - 4e^{0.65}y = x

You can then solve the quartic for y, and from there take logs to find t.
Original post by DFranklin
It has an analytic solution, but it's going to be horrible.

If you set y = e^{-t/40}, then you have

e1.7y4−4e0.65y=xe^{1.7}y^4 - 4e^{0.65}y = x

You can then solve the quartic for y, and from there take logs to find t.

Ah, excellent - thanks very much! After I posted this thread I had to go out for half an hour, and was thinking roughly along those lines whilst out and about

Original post by thecakeisalie1
change it into logs and see what happens

I don't think there's a way to take logs with useful results from the equation in the form that I posted it. Thanks, though :smile:

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