Verified answer

In a way you already know this.

For example you know that

10 * 10 = 10^2 = 100 and that

10 * 10 * 10 = 10^3 = 1,000

You probably already know that the numbers

2 and 3 are often called power or exponent.

But here is the bit you might have missed.

A third name for that number is log.

Yes, a logarithm is just a power.

10^3 = 1,000 tells us that

10 to the power of 3 is 1,000 or

with BASE 10 to get 1000 the POWER is 3 or

the POWER to BASE 10 of 1000 is 3

Now replace the word power with the word log

The log to BASE 10 of 1000 is 3

So the logarithm of a number to a given base

is the POWER to which the base must be raised

in order to produce that number.

OK so far ?

The base will not always be 10.

Suppose the base is some number represented by b

and we get y by raising b to power x

We write this y = b^x

Then the POWER to BASE b of y is x

We write this log(base b) of [y] = x

Read that line again so that it sinks in.

Now you are beginning to understand logs.

So why introduce a new word (and a slightly

different way of using it), when we already had power ?

Well, one reason is that we want to be able to deal with

powers, (logs) that are not whole numbers, like 0.30103

How would you work out the answer to

log(base 4) of [8] = ?

Really this asks "what power do you have to raise 4 by to get 8?"

Well, 4 is 2^2 and 8 is 2^3,

so [2^2]^(3/2) = 2^3 or

4^(3/2) = 8

Now we can express that statement as a logarithm

log(base 4) of [8] = 3/2 = 1.5

For many results your calculator gives the answer

for example log(base 10) of [2] ~ 0.30103

There is more to learn, such as the properties and

rules for logs and the use of the base e, so for the

next steps see this series of helpful webpages.

http://www.themathpage.com/aprecalc/logarithms.htm...

I hope that got you started,

Regards - Ian

here's a simple example:

since 10 to the third power is 1000 (10X10X10=1000), the log base 10 of 1000, is 3.

In other words, 10 to what power gives you 1000? That answer is 3.

Similarly, log base 10 of 100 is 2 since 10^2=100.

log base 10 of 10000=4 since 10^4=10000.