1.)How can i convert Logarithm(log) to a Natural Logarithm(ln)?

Question

log(2) = ln(2)/ln(10)
So, ln(2) = log(2) x ln(10)
or ln(2) = log(2) x 2.303
Just remember this multiplying factor '2.303'.
* For converting ln to log, divide ln(x) by 2.303
* For converting log to ln, multiply log(x) by 2.303
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>where's that 2.303 came from?
>kindly explain further. tnx
:D

Answer 1

To convert a log in base b to a log in base a, you divide by log(a). The answer given is showing you this:

ln is just a log base e, where e=2.718281828...

So, to convert log base b, where b is any number at all, including 10, we do:

log base b of x = ln(x)/ln(b)

Frankly, the given answer says all this. The only point of confusion you seem to have is not realizing that 2.303 is just ln(10). Read the answer you posted one more time a bit more carefully, and it will become clear.

Answer 2

ln(10) = 2.30258509

log(x) = ln(x) / ln(10)
ln(x) = (log(x) * ln(10)

(You just substitute the 2.303 for ln(10))

The natural log is base e,
log is base 10.