what exactly is a log?
could you define what logs are used for and why?
what does it mean to have something log based 10?
A logarithm of a number N (to remind us it is the number), is the power
(exponent), lets call it L (to remind us it is called the logarithm) that
a number, let's call it B (to remind us it is called the base) must be
raised to equal N. So, symbolically this can be written:
B^L =N so the log (N) to the base (B) is L. A couple of examples makes
it clearer than trying to give a this general symbolic expression, which
is really clumsier than the concept itself.
1000 = (10)^3 so 3 is the logarithm of 1000 to the base 10. The symbol "^"
means raised to the power of.
This is written: log10(1000)=3
16 = (2)^4 so 4 is the logarithm of 16 to the base 2.
This is written: log2(16) = 4
Base 2 logarithms are used in computers a lot because computers ultimately
come down to two choices
1 or 0. So you may have seen the number 1024 crop up in a lot of stuff
about computers. It is:
1024 = (2)^10 or 10 = log2(1024)
See! Taking a logarithm is just the opposite, the inverse function, of
taking a power. It is the "un-power" of a number.
The base number can be any number that is convenient as long as it is
clear to the reader what it is. In fact, a base that keeps turning up in a
lot of math, physics, and chemistry is the base number, e , where
e = 2.718281828... is a number whose decimal expression never repeats
itself, although it might not look so by only looking at the first 9
digits, but trust me, it just starts wandering off into "number-number land".
So we can write:
loge (6) = 1.791759469... Because this base is very common, although it
seems a little wierd, it is given a special symbol "ln" . So ln(6) =
Click here to return to the Mathematics Archives
Update: June 2012