Question

How do you calculate \[\ln 23\]?

Answer 1

Hint: The natural logarithm (ln) is the logarithm to the base of e and also called the inverse of the exponential function. ‘e’ is an irrational number that is a constant and its value is 2.718281828459. It can also be written as \[{{\log }_{e}}x\]. \[\ln x\]is undefined when \[x\underline{<}0\].

Complete step by step answer:
We can calculate ln23 using an ln calculator. First ON the calculator and then press the button ln and then enter the value to be calculated. Now press the button = or press the button ANS to get the answer.
The answer displayed on the screen will be
\[\Rightarrow \ln 23=3.13549421593\]
We can also find the value of ln23 by using natural logarithm tables. There are two tables in natural logarithm tables one is for values greater than 1 and the other is for less than 1. Since our value is greater than 1, we check the table greater than 1 and write the value.
From the table, the value of ln23 is
\[\Rightarrow \]\[ln23=3.13549.\]
Similarly, another logarithm table is also present for values less than 1.


Note:
We can directly find the logarithmic value by taking the image of the graph of the exponential function graph with respect to any of the lines \[y=\pm x\] based on the existence of the graphs.
Let \[y=\ln 23\] \[\Rightarrow y=\ln 23={{\ln }_{e}}23\to {{e}^{y}}=23\]
By plotting a graph \[{{e}^{y}}=23\] and taking the image of this with respect to \[y=\pm x\] gives the value. We should be thorough with the logarithm and exponent concept to avoid mistakes like taking base 10 for \[\ln \] function instead of e.