what does log mean on a scientific calculator

This may not be in purely mathematical terms but I'll explain it the best I can.

The way I understand it, log is basically a query as to what power a number must be raised by for it to become another number.

So basically, you start with something like this:

$$y^x=z$$

and turn it into a log like this:

$$log_yz=x$$

The small number between the log and the z in this equation is called the base. The default base of any log is 10 unless specified otherwise, so when you press the log button on the calculator followed by 100 for example and see this:

$$log100$$

you'll get 2 when you press "=", because 10 to the 2nd power is 100.

For example:

$$log_28=3$$ is the same as saying $$2^3=8$$.

And like I said above, $$log100=2$$ because $$10^2=100$$ and there was no base specified in the log, so the default base is 10.

Hope this clears things up for you :)

Excellent answer anonymous.  

Why don't you join up ?   It is super easy.  

So basically a log is a power (index or exponent)

Almost whenever you need to solve an equation where the unknown is an exponent then you will need to use logarithms.     

You may be interested to work through this unit.   

http://www.mathsisfun.com/algebra/logarithms.html