Solve the equation $2^{x^2 + x} + \log_2x=2^{x+1}$ 
Solve the equation $2^{x^2 + x} + \log_2x=2^{x+1}$ where $x$ is real.

I tried to use derivatives, without success.
It's obvious that $x=1$ is solution. 
Also, if $x \gt 1$ then $2^{x^2 + x} \gt 2^{x+1}$ and $\log_2x \gt 0$ therefore the equation has no solutions $x \gt 1$.

Similarly, for $0 <x<1$, we have $2^{x^2+x} <2^{x+1}$ and $\log_2{x} <0$
So, $x=1$ as for $\log_2{x}$ to be defined we must $x>0$
