How does a calculator calculate logs (of base 10 and 2)?

Question

How does a calculator calculate logs (of base 10 and 2)?

Answer 1

Surely you know that e (2.718281828...) can be evaluated by a series:
e= 1/0! + 1/1! + 1/2! + 1/3! ...

Well, there are series that do converge to the natural logarithm, some are tweaked to converge to 10 or 15 decimals (i.e. the required accuracy of a calculator) in just a few terms. That is how a calculator evalutes logarithms, usually the natural (base e)
Once you have the Log-e, it is easy to transpose that value to another base, since

Log 10 (x) = Log e (x) / Log e (10)

In order to speed up calculations, the calculator CPU will have some key and frequently used factors permanently etched in the CPU memory.

Answer 2

Log Base 10 Calculator

Answer 3

in a scientific calculator there only 2 buttons are for Logarithm calculation:

1. "log" button: is to calculate log base 10 (known as Common Logarithm)
2. "ln" button : is to calculate log base e (known as Natural Logarithm)




now to calculate log base 2, you can use any of these two, but whichever, you gonna need to convert it into base 2.

You can do this by dividing your result by the "log" or "ln" of base 2.

e.g:
If you to calculate log(x) base 2, then calculate log(x) base 10 then divide it by log2 or to calculate ln(x) base 2, do it with base 10 then divide it by ln2.

example calculation:
log8 base 2 is 3. using calculator is should be log8 base 10 / log2 .


thank you :)

Answer 4

if you are computing Log of x to the base 10, simply press Log x.

if you are computing Log of x to the base 2, press Log x divided by Log 2.

1) example, log 3 to the base 10, press Log 3.
2) example log 3 to the base 2, press log 3 divided by log 2.

I hope this helps.

Answer 5

log key is base 10 ln key is base 2

Answer 6

Interesting topic!

Answer 7

Formula.

Please see the below article.