[1] They don't say what base though. 2? 10? e? Maybe one of the
researchers was a computer scientist, one was an engineer, and
one was a mathematician, so they couldn't
decide.
First, an algebra review:
log(base,a)==log(other_base,a)/log(other_base,b) [Equation 1]
Meaning that you can convert a logarithm from one base to any other
base by dividing by a constant value (log(other_base,b)), or
multiplying by the inverse of the same constant.
Now, suppose you have found that the minimum number of links between
any 2 web pages (just an example ;) varies according to this
formula:
links==x*log(2,number_of_public_web_pages)
where x is an unknown constant, and 2 is the base of the log.
Suppose you want to represent that in base 10 logs. This means you
need to divide by log(2,10) (to change the base), and, to keep the
equation balanced, multiply by log(2,10) :
links==x*log(2,number_of_public_web_pages)
links==x*log(2,10)*log(2,number_of_public_web_pages)/log(2,10)
Since:
log(2,number_of_public_web_pages)/log(2,10)==log(10,number_of_public_web_pages)
[See Eq 1]
links==x*log(2,10)*log(10,number_of_public_web_pages)
Still a logarithmic equation. Furthermore, since x is an unknown
constant, x*log(2,10) is also an unknown constant. Let us call it
x2:
x2==x*log(2,10)
links==x2*log(10,number_of_public_web_pages)
Since you know niether x nor x2, does it matter whether this log is
base 2 or base 10?
Wait, there's more. First, let us go back to the original equation:
links==x*log(2,number_of_public_web_pages)
Now, imagine an unknown constant y such that 1/log(y,2) == x :
x==1/log(y,2)
and plug it in place of x:
links==log(2,number_of_public_web_pages)/log(y,2)
By equation 1, we have:
log(2,number_of_public_web_pages)/log(y,2)==log(y,number_of_public_web_pages)
So
links==log(y,number_of_public_web_pages)
Which means you do not know the base in the first place ... So why
pretend you do?
[ Parent ]

