What is use of logarithm in maths?

Answer 1

Logarithms is an extremely versatile function.

Originally, logarithms were used to simplify calculations. In days gone by, navigational tables required a huge number of calculations. Many of these calculations entailed multiplications of numbers with several (4-5) digits. This required people who were able arithmeticians.

However, transform the number to their logarithms. Then the process of multiplication is replaced by addition. Many more people can add together two 5-digit numbers than multiply two 5-digit numbers. So do the addition and then use a table to look up the antilog and you have the answer. It was much easier (and cheaper) to employ a large number of people who could perform these additions reliably.

A second, major role of logarithms is that they are the integral of the reciprocal functions. Many algebraic fractions can be restated as a sum of partial fractions which are all reciprocals of binomial terms. So the integral of the original fraction is the sum of the terms of the corresponding partial fractions. There are also other functions for which logs are required.

A logarithm is the inverse function to exponentiation. Compound interest or depreciation, radioactive decay, [unrestrained] population growth are all examples of exponential change over time. The increase (or decrease) over a known period of time can be calculated using the exponential function but you need the logarithmic function to calculate the time required for the variable in question to reach a specified threshold.