Chapter B.1, Problem 21E

(a)

To determine

Show that $\ln x$ grows slower as $x\to \infty$ than $x^{1/n}$ for any positive integer n.

(b)

To determine

The value of x greater than 1 for which $x^{1/1000000}>\ln x$.

(c)

To determine

The value of x at which the graphs of $x^{1/10}$ and $\ln x$ cross or equivalently.

(d)

To determine

Show the value of x at which the graphs of $x^{1/10}$ and $\ln x$ cross or equivalently in graph.