Chapter 3.2, Problem 3E

To determine

To find: The appropriate words to fill in the blanks.

Answer to Problem 3E

Natural, $\ln x$.

Explanation of Solution

Given information:

A statement is given as -

"The logarithmic function $f(x)=\ln x$ is called the ________ logarithmic function and has base ________.”

Calculation:

The function $f(x)=y={\log }_{a}x$ is defined as logarithmic function where $y$ is called exponent and $a$ as base. Also, $x>0,a>0\text{ and }a\ne 1$ .

The equivalent exponential form of the logarithmic function will be $a^y=x$ . i.e.

  $a^y=x\Rightarrow {\log }_{a}x=y$ .

When base is taken as $a=10$ then it is called common logarithm and denoted as $f(x)=y=\log x$ .

When base is taken as $e=\mathrm{2.7182...}$ , then it is called natural logarithm and denoted as

  $f(x)=y=\ln x$

Hence, appropriate words to fill in the blank would be −

Natural, $\ln x$.