The Logarithm

If raising something to a power means making a base multiply itself exponent times, the logarithm is the inverse of this.

Let's suppose that we have the square of 3:Now, we define the logarithm. Logarithms have a base. When we say, for example, the base-3 logarithm of 9 is equal to x, we are implying that this x is the power the base, 3, is raised to to yield 9.

So, what is the base-3 logarithm of 9?This is the same as saying:Substituting, we get:Indeed, the base-3 logarithm of 9 is equal to 2.

The general definition of the logarithm is:By the rules of powers, the following are defined as The logarithmic laws:

A special case of the exponential and logarithmic functions is important to learn:
Euler's Number, The Exponential, The natural logarithm