# Why we use logarithm?

##### 1 Answer

Some thoughts...

#### Explanation:

I am not sure what the context of your question is, but logarithms - especially the natural logarithm - occur naturally in a variety of circumstances.

The natural logarithm

When you get onto calculus, you will find that the natural logarithm occurs as the integral of

#int 1/x dx = ln abs(x) + C#

Logarithms are the basis upon which slide rules work.

On a practical note, logarithms allow us to express on a linear scale the measure of physical properties that vary exponentially.

For example, the pH of a solution is

Another example would be decibels, which are a logarithmic measure of loudness.

If you are trying to create a model of experimental data that you suspect is exponential, then you would typically take the logarithm of measured values against a variety of input values, then use linear regression to find a line of best fit. Then reverse the logarithm by taking the exponential of that line to get an exponential curve of best fit for your data.