This post, I play with my mathematics experience on logarithms. I win many math contest before and I badly needing it now 
. I assume that PR toolbar is a logarithmic value as a function of the number of links of an unknown base “X”:
PR tool bar = log (Backlinks) to the base X
where “Backlinks” is the total amount of backlinks from other domains pointing to the entire site.
“Base x” is the base of the logarithm not being solved so far. It is used to convert the actual back link data to a friendly Google Page rank measurement we seen in their toolbar, which will update every 3 months.
In this post I would like to calculate the value of “x”. So my objective will be to calculate the base of the logarithm used by Google to export it to the toolbar. Though this is not guaranteed to be accurate because the tool bar data is just a snapshot in time, it is not a real time one. So to define variables:
PR tool bar = log (Backlinks) to the base X , can be written as:
x ^ PR tool bar = backlinks , by principle of logarithm
then, taking the logarithm of both sides of the equation:
PR tool bar * log x = log (backlinks)
All logarithms are assuming at the base 10 above.
Then :
Log x = (log (backlinks))/ (PR toolbar)
Say we will equate:
Y = (log(backlinks))/ (PR toolbar)
Finally we can solve for x as:
x = 10 ^ Y
By principle of relationship in converting logarithmic to exponential and vice versa.
I do not know the value as it needs to gather actual data. But the principle is presented above.
