# How to solve mixed power and exponential equation?

The exercise says that I should find "real zeros" of the following function:

$$f(x)=7-2x^2+2^{-x}$$

I have tried several ways, but I keep getting stuck as I take log-s of both sides. Can I solve this equation manually, somehow, not in a very complicated way?

(I suspect, it shouldn't be very hard, since it's in the introductory chapter of the calculus book :/)

• Rendering a plot, the function seems to have three non-integer zeros. The exercise must have a typo, because there is no elementary way to solve the equation, that is, the solutions can't be expressed as expressions using elementary functions. Perhaps you only have to prove that it has exactly three zeros. – ajotatxe Apr 17 at 7:43
• Unfortunately, there is another similar equation too.. Anyway thanks, I won't make any moore effort to solve this :/ – ანო ანო Apr 17 at 7:50