## Monday, 6 February 2017

### Logarithms

To understand the rules of logarithms we have to understand indices.

In this example, the number 4 is the power or the exponent. The number 2 is the base.

An alternative way to write this expression is illustrated below.

This shows us the first rule of logarithms.

We know that anything to the power of one is itself, like the expression below.

The version of the above expression logarithmically is shown below.

We have now found the second rule of logarithms.

The third rule of logarithms is shown below.

Consider this question.

Following the third rule of logarithms where x is 2 and y is 4, we see that

The fourth rule of logarithms is with regards to powers in log expressions.

Consider this expression.

Following the fourth rule of logarithms, we see that

The fifth rule of logarithms goes as follows:

Consider this expression.

The expression can be rewritten as shown below.

as 6 divided by 3 is 2.

The last log rule you need to remember is shown below.

as