Number of Non-Negative Real Roots

Equation: $2^x - 1 = x$. For $x = 0$, $2^0 - 1 = 0 = x$. For $x = 1$, $2^1 - 1 = 1 = x$. For $x = 2$, $2^2 - 1 = 3 \neq 2$. By testing or taking derivatives, $f(x) = 2^x - x - 1$ is strictly convex for $x > 0$. Thus, it can have at most 2 real roots. The non-negative roots are $x = 0$ and $x = 1$. Hence, there are 2 roots.