Question

can you you explain logarithm functions to me?
@Yttrium

Answer 1

Well looking up the dictionary definition, we get:
"the exponent of the power to which a base number must be raised to equal a given number; log: 2 is the logarithm of 100 to the base 10 (2 = log 10 100)"
That certainly clears things up huh?
Probably not.

Answer 2

Time for more explanation.
Logarithms are the exponents to which a number must be raised to obtain that number.
the log of 10 is 1
the log of 100 is 2. Why two? Because 10² = 100
the log of 1,000 is 3 because 10^3 = 1,000
Do you know what the log of 10,000 is?

Answer 3

A logarithm is defined this way:
\[\log_{a} b=c <=> a ^{c}=b\]
Now, it's very easy to write it in a mathematical form, but for those who are not used to it, cannot see it clearly, so we'll look at an example and observe it:
Let's take Wolf's example:
\[\log_{} 100\]
the number that goes in the lower aprt of the "Log" is called the "base" and when we don't write it down it means that we are using "10" as a base.
So the logarithm is saying the following:
"With what exponents wich base is 10 gives me a result of 100?"
so we can transform it, based o nthe definition:
\[\log_{}100 <=> 10^{x} =100\]
I explained to you earlier how you can play around with the exponents to simplify:
\[10^{x}=10^{2}\]
so, because of the exponential property that states, if I have same bases then I can make the exponents equal:
\[x=2\]
and there we got it:
\[\log_{} 100=2\]
Thet's pretty much the "definition" of a logarithm, of course, with a definition comes theorems and properties wich in future will be seen.

Answer 4

All the examples I gave have been powers of 10, but there are many numbers besides those. So, for example, what is the logarithm of the square root of 10? (which is 3.1622776602)
It is .5 because 10^.5 = 3.1622776602

Answer 5

See Khan's videos
http://www.khanacademy.org/math/algebra/logarithms-tutorial

for the basics.

And then, for functions, see
http://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/log_functions/v/solving-logarithmic-equations_DUP_1