Find the value of $x$ in this equation. $2^x -x=5$
I can't solve this equation, but I can see that $x=3$ (through trial and error) but I don't know how to attain the value $3$.

$$2^x - x=5 \implies 2^x  = 5+x$$
It is trivial to see that for $x>3$ , 
$$2^x > 5+x$$
Hence we are only left with $3$ possibilities for $x\in \mathbb {N}$ , which yields $3$ as a solution to the equation.
For $x \in \mathbb {Z}$ , we observe that for $x<-5$,
$$2^x > 5+x$$
Hence the only useful range for the solution is $[-5,3]$ which can be found using trial and error.
