# What is a Logarithm

## Laws of Logarithms - How it Works - Video

### Logarithms - What are they

Logarithms:

Logarithms is fancy way we can write multiplication and faster sometimes. Logarithms is how many of this number do we multiply to get that number using powers.

How many 2s multiply together to make 32? Well, we multiply 5 of the 2s to get 32.

2 * 2 * 2 * 2 * 2 is 25 and 25 is 32. Using logarithms we can write as log2 32 = 5.

Here we have log2 32 = 5. We can say several ways.

• The logarithm (log) of 32 with base 2 is 5

• The logarithm (log) base 2 of 32 is 5

• The base 2 logarithm (log) of 32 is 5

Here we have log3 81 = 4. We need to work backwards to create our logarithm. The result 4 is telling us how many times some number is multiplied to get 81.

We use the base in this case 3 and raise it to the power of our result, 4, and that equals the logarithm. So we can write log3 81 = 4 as 34 is 81.

### Laws of Logarithms

Laws of Logarithms:

Here we have the different laws of logarithms. We will go into further detail here.