Question

How do you evaluate $\ln 5.42$ using a calculator to four decimal places?

Answer 1

Hint:
In this question, we want to find the value of the natural logarithm using a calculator to four decimal places. The most frequently used base for logarithms is e. Base e logarithms are important in calculus and some scientific applications; they are called natural logarithms. The base e logarithm, ${\log _e}\left( x \right)$, has its own notation, ${\text{ln}}\left( x \right)$. The natural logarithm of a positive number x satisfies the following definition: for $x > 0$, $y = \ln (x)$is equal to ${e^y} = x$. We read ${\text{ln}}\left( x \right)$ as “the logarithm with base e of x” or “the natural logarithm of x”.
Steps to find the natural logarithm using the calculator are as below.
Given a natural logarithm of the form $y = \ln (x)$.
1) Press [LN]
2) Enter the value given for x.
3) Press [ENTER]

Complete step by step solution:
In this question, we want to find the value of the natural logarithm using a calculator to four decimal places.
The given natural logarithm value is,
$ \Rightarrow \ln 5.42$
Let us compare the above equation with $y = \ln (x)$.
Here, the value of x is 5.42.
Now, the first step is to press[LN]. On most graphing calculators, there is a “shift” or “second“ button and the button that says ${e^x}$. The reason we press the “second” or “shift” button is that this tells the calculator to apply the inverse of ${e^x}$ which is $\ln \left( x \right)$.
Now, the second step is to enter the value given for x. In this question, the value of x is 5.42.
Therefore, to type in the value of x is 5.42. Type this value in the parenthesis.
Now, the third step is to press [ENTER].
Hence, we will get the answer.

Note:
Make sure that the calculator has in the natural logarithm mode. For that, we have to press the “shift” or “second” button. When we enter the value we want to find that must be written in the parenthesis.