What is the necessity for using log and ln in mathematics?

Answer 1

log is the representation or say short form of logarithm and the basic principle of logarithm is that
a^x = m
=> log m (base 'a' written as subscript between log and m) = x
for e.g: 10 ^2 = 100 (exponential form. )
=>log 100 (base 10 ) = 2
these are logarithms with base 10 but ln is natural logarithm with base e .and by this time u would have got the value of e = 2.7182818
and to convert ln to log
ln (x) = 2.303 log(x)

Why 2.303? Let's use x = 10 and find out for ourselves.
Rearranging, we have (ln 10)/(log 10) = number.
We can easily calculate that ln 10 = 2.302585093... or 2.303 and log 10 = 1.
So, the number has to be 2.303. Voila!

Answer 2

Oh, jeez, so many. I can tell you about some applications in the statistics arena.

The log transformation is used quite a bit if the data is skewed to the right (meaning that if you look at a picture of the distribution of the data, it has a tail to the right). Taking the log make the distribution more symmetric.

That is why logarithms are used in the calculation of the confidence interval for odds ratios. It's kind of hard to describe what that is here. I'll put a link below. Also, since odds ratios are strictly nonnegative, taking the log gets you any value on the real line, which makes it easier to work with in this case.

Logarithms are used as a method for maximizing likelihood functions. Sometimes finding the maximum of a function f(x) is hard to do. Since the log function is a strictly increasing function, you can find the maximum of log f(x) and that maximum will be the same as the maximum of f(x). Often in statistics, finding the maximum of log f(x) is easier.

There is also a distribution called the log normal, so named because if log X follows a normal, then X follows a log normal.

It is also used in logistic regression. Can't be done without it! (link below)

There are definitely a lot more, even in stats.

Answer 3

Logarithms in general are simply the "reverse" of exponential operations, and thus are often used in conjuction with them. For example, whereas 10^3=1000, we also say log10(1000)=3.

Ln is the natural logarithm using a base of e=2.7182818... and is used for a variety of circumstances, usually having to do with continual exponentiation, such as with compount interest and population growth.

Answer 4

well log generally makes numbers which are very large more managable. ln is generally useful for inverting expressions with the function e^x which appears in lots of equations for exponential growth/decay (e.g. damped oscillations or radioactive decay).

Answer 5

while workin out graphs any fns having a large change on y axis for a change on x axis cozes problem but taking its log solves the problem coz a gr8 change only causes little change in final value

Answer 6

Well, one of main reasons is to be able to solve exponential functions.