Does $f(x)=ax^b$ grow faster than $g(x)=\ln x$ for all $a, b > 0$? Can I say that $f(x) > g(x)$ as $x$ approaches infinity?
I thought the answer is yes, but this graph appears to be telling a different story.
Is the polynomial (the green curve) going to cross the log function (the red curve) and exceed in value for some large value of x?
If the answer is yes, does it mean that if I subtract the two functions and set it to zero, the resulting equation will have two roots? What are the roots?