How to calculate ln &#x2061;<!-- ⁡ --> ( x ) I know only to calculate ln &

Oakey1w

Oakey1w

Answered question

2022-06-10

How to calculate ln ( x )
I know only to calculate ln ( ) using a calculator, but is there a way to calculate it without calculator:for example: ln ( 4 ) = ? ? as far as I know the only way to do so is to draw the graph of l n but it primarily depends on values from calculator. So really is there some formula for ln ( ) to calculate its exact value for a specific number?

Answer & Explanation

Tianna Deleon

Tianna Deleon

Beginner2022-06-11Added 29 answers

You can use the following definition for the natural logarithm:
ln t = 1 t 1 x d x .
So ln t represents the area below the graph of 1 / x from x = 1 to x = t. You can easily approximate this area using the Trapezium Rule or other similar approximation methods.
arridsd9

arridsd9

Beginner2022-06-12Added 12 answers

You could use it Taylor Series.
Define
ln ( y ) = ln ( 1 x ) = k = 0 x k k
Then you are able to calculate the logarith for all real numbers y > 1 with y = 1 1 x
For real numbers 0 < y 1 you could use
ln ( y ) = ( y 1 ) ( z 1 ) 2 2 + ( z 1 ) 3 3
instead

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