Logs and Exponentials

?

Exponentials:

Exponential functions and their associated rules are something that you are familiar with. 

By this, I mean that an exponent is essentially and indice, and thus can have the same rules applied to it.

Introduction to 'e':

The function of:               is a specific exponent which play a huge role it maths.

'e' is approximately 2.71828.

What is a log?:

Logarithms come in the form \log _a x (http://www.bbc.co.uk/staticarchive/91ece3199d19bf25812db14664c8aab9afd87a4c.gif). We say this as "log of x (http://www.bbc.co.uk/staticarchive/20680cb107766b2e03c23e79daa552b5e1881e05.gif) to base a (http://www.bbc.co.uk/staticarchive/f0b83f969ad64d1b9d4be3459b2d354dc1a96e80.gif)". But what does \log _a x (http://www.bbc.co.uk/staticarchive/91ece3199d19bf25812db14664c8aab9afd87a4c.gif) mean?

Consider the following examples.

  • \log _5 25 (http://www.bbc.co.uk/staticarchive/ae5f3a627644f11f1c42df1f76d5e4326808f94e.gif) means "What power of 5 (http://www.bbc.co.uk/staticarchive/5791c369cf9b194a1874c8395c8d5da6bf6dac12.gif) gives 25 (http://www.bbc.co.uk/staticarchive/145d8abf48386528a4ac179adbd076c0eeb10ddb.gif)?"

    The answer is 2 (http://www.bbc.co.uk/staticarchive/577691effb25bd2108735e46de25a50fa0bbcd75.gif) because 5^2 = 25 (http://www.bbc.co.uk/staticarchive/8511a14372232be3d8e6347b7e07838d18d692f3.gif), in other words \log _5 25 = 2 (http://www.bbc.co.uk/staticarchive/0d1b8e6fe7fc228ddaa4523dc4156847c51ad6aa.gif)

  • \log _2 16 (http://www.bbc.co.uk/staticarchive/6fe9c97ece5f3389a522afbcd7e4af450427f9bb.gif) means "What power of 2 (http://www.bbc.co.uk/staticarchive/577691effb25bd2108735e46de25a50fa0bbcd75.gif) gives 16 (http://www.bbc.co.uk/staticarchive/f37b2bdf96ce18b277e19783f9221a047ebb6d9f.gif)?"

    The answer is 4 because 2^4 = 16 (http://www.bbc.co.uk/staticarchive/5f6130309c4689ddab57e6cc07a3190ae3c1a58b.gif), in other words \log _2 16 = 4 (http://www.bbc.co.uk/staticarchive/f0ea5785c25dbd8ca248a187932c5151841a17b8.gif)

Indices:

Comments

No comments have yet been made