# Exponents and logarithms¶

## Exponents¶

## Logarithms¶

### Introduction¶

A logarithm is defined so that log_b(w)=z such that w=z^b. A logarithm has two parameters – a base. It value of the logarithm is you what you need to raise the base to to get the value of which the logarithm is taken.

### Some notation and the definition of Euler's number¶

In mathematics ln(x) and log(x) are both taken to mean log_e(x), where e is an irrational mathematical constant called Euler's number and can be defined in different ways.

The infinite decimal of e begins 2.718281828459045\dots.

### Properties of logarithms¶

Much like the properties of powers there are also useful properties of exponents.

### Converting products to sums with logarithms¶

It is often easier to compute the value of a summation than it is to find the value of a product. Using the property of logarithms log(xy)=log(x)+log(y) it is possible to rewrite a product as a sum. (This example is taken from Chapter 1 of Stephen J. Miller's *The Probability Lifesaver* (ISBN: 9780691149554))

Taking the logarithm.