What Is the Natural Logarithm?

The natural logarithm (e logarithm) ln (x) works the same way as the common logarithm when it comes to uses in equations. Like all logarithms, it follows the same rules as the rest.

Its appearance is also very similar. The only difference is that log (x) has 10 as the base number, which means 10logx = x, whilst ln (x) has e as the base number, so eln x = x. The natural logarithm got its name because it has the natural number e as the base.

Theory

The Natural Logarithm

The logarithm ln is a function. When you take the natural logarithm of a number (a) you will get a new number k. The number k

k = ln (a),a > 0

is so that

ln ex = xandeln x = x

In this figure you can see the graphs of the common logarithm and the natural logarithm. Both cross the x-axis at x = 1, but ln x grows slightly faster than logx.

A graph showing the difference between the common and the natural logarithm.

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