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Re: exponential equation
To prove that there are no more we maybe can use calculus here.
2) For this one there looks like there is one root near - 1 / 2. ( see the last image )
3) There looks like there is one root around - 3 / 5. ( see the first image )
As a general rule when an exponential function begins to overpower a polynomial, the polynomial never recovers. I would say that there are no more roots.
In mathematics, you don't understand things. You just get used to them.
No explanations, just DGA.
If you can not overcome with talent...overcome with effort.