Question

How do you evaluate ln 0.1 using a calculator to four decimal places?

Answer 1

Hint: For this question, you just need to have a calculator or a scientific calculator. You just need to type in the values in the calculator and then round it off to four places and finally, you get the answer in the calculator.

Complete step by step solution:
In the given question we are asked to evaluate ln 0.1 using a calculator to four decimal places.
To solve this, we will need a normal calculator or a scientific calculator. You can even use the calculator application on any device such as mobile phone or computer.
Next, we have to type in the values. For this given question, we have to type the values as $ \ln \left( 0.1 \right)$. For this, first we have to type ln function in the calculator and then type in the 0.1 value in the calculator.
After doing this, the calculator shows the answer as,
$\Rightarrow \ln \left( 0.1 \right)=-2.30258509$

But we need to round off the answer to four decimal places. To do this, we first look at the fifth place. If the value at fifth place is greater than or equal to 5, then the value at fourth place increases by one, otherwise, it remains the same. In the above answer, we have 8 in the fifth place. Therefore, we have to increase the value at fourth place by 1. Therefore, we get the answer as
$\Rightarrow \ln \left( 0.1 \right)=-2.3026$

So, therefore, by evaluating the given question that is $ \ln \left( 0.1 \right)$ we get the answer as $ \ln \left( 0.1 \right)=-2.3026$.
Therefore, the solution of the given equation $ \ln \left( 0.1 \right)$ is $ \ln \left( 0.1 \right)=-2.3026$.

Note: In this question, you need to be careful while typing the values in the calculator. You might confuse between log and ln. You could also verify the answer by finding the value of ${{e}^{-2.3026}}$.