Details of logarithmic calculations?

[kiru]

Main Question or Discussion Point

From where I can get the details of lograthmic calculations?How the values are found?and on what basis?

 

[Jameson]

Do you want to know for instance how $$\log{3}$$ is found? That kind of calculation?

 

[kiru]

Do you want to know for instance how $$\log{3}$$ is found? That kind of calculation?

Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?

 

[Werg22]

Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?

I would have the same question + how cosines are calculated.

 

[HallsofIvy]

There are a variety of ways.

The simplest is to use "Taylor's Series". It can be shown, in Calculus, that for x between 0 and 2, ln(x)= (x-1)- (1/2)(x-1)²+ (1/3)(x-1)³-...- ((-1)ⁿ/n)(x-1)ⁿ+... That infinite series does not converge very fast but it will give close to the correct value eventually.