Chapter 4.3, Problem 14E

(a)

To determine

To find: The logarithm form of the given exponential function.

Answer to Problem 14E

The logarithm form is ${\log }_{10}1000=3$ .

Explanation of Solution

Given:

The given equation is ${10}^3=1000$ .

Calculation:

Consider the exponentialfunction is,

  $a^y=x$

The, the logarithm form of the above exponential equation is,

  ${\log }_a=y$

For the given equation ${10}^3=1000$ , the logarithm form is,

  ${\log }_{10}1000=3$

Thus, the logarithm form is ${\log }_{10}1000=3$ .

(b)

To determine

To find: The logarithm form of the given exponential function.

Answer to Problem 14E

The logarithm form is ${\log }_{81}9=\frac{1}{2}$ .

Explanation of Solution

Given:

The given equation is ${81}^{\frac{1}{2}}=9$ .

Calculation:

Consider the exponential function is,

  $a^y=x$

The, the logarithm form of the above exponential equation is,

  ${\log }_a=y$

For the given equation ${81}^{\frac{1}{2}}=9$ , the logarithm form is,

  ${\log }_{81}9=\frac{1}{2}$

Thus, the logarithm form is ${\log }_{81}9=\frac{1}{2}$ .