Chapter 7.8, Problem 6E

(a)

To determine

Whether the given function ${\log }_2\left(x^2\right)$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(b)

To determine

Whether the given function ${\log }_{10}10x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(c)

To determine

Whether the given function $\frac{1}{\sqrt{x}}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(d)

To determine

Whether the given function $\frac{1}{x^2}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(e)

To determine

Whether the given function $x-2\ln x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(f)

To determine

Whether the given function $e^{-x}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(g)

To determine

Whether the given function $\ln \left(\ln x\right)$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(h)

To determine

Whether the given function $\ln \left(2x+5\right)$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.