Home > Algebra > Equation & Roots

## Equation & Roots

How many roots does the equation $2^x=x^2$ have?
Solution: For $x > 0$ and take logarithm on both sides. We get $x \ln 2=2 \ln x$ which is equivalent to $\frac{\ln x}{x}=\frac{\ln 2}{2}$, which has at most 2 solutions, since the function is increasing on $(0,e)$ and decreasing on $(e,\infty)$.
On the negative side there is exactly one solution.