Chapter 11.4, Problem 10ES

To determine

(a)

To prove:

Use the definition of logarithm to show that ${\log }_b{b}^x=x$ for all real numbers x.

To determine

(b)

To prove:

Use the definition of logarithm to show that $b^{{\log }_{b}x}=x$ for all positive real numbers x.

To determine

(c)

Use this result to show that ${\log }_b$ and ${\text{exp}}_b$ (the exponential function with base b ) are inverse functions.