How to find the % of a value on a Y axis of a LOG graph?

Wow, this one is though!

I'm trying to find in PHP the % of a value relative to the Y axis. If we refer to this graph : http://en.wikipedia.org/wiki/Semi-log_graph (2009 outbreak of influenza A), let's say that I want to find what % is a value "256" on the chart.

Visually, it's easy : it's a bit more than a 1/3 or 33%. If 开发者_运维百科we look at the 1024 value, it's around 50% of the height of the Y axis. 131072 would be 100%.

So how do I calculate this with PHP?

Let's take this graph and take X = day 0 and Y = 256. What is 256 as a % of Y ?

Thanks a lot to anyone can compute this baby :)

percent = 100 * ( log(y) - log(y1) ) / ( log(y2) - log(y1) )

where

y = value 
y1 = smallest value in y-axis
y2 = largest value in y-axis.

when y1 = 1.0 then you can simplify the other answers given here (since log(1)=0 by definition)

percent = 100 * log(y)/log(y2)

Note that not all log charts have 1.0 as the lowest value.

ln(131072) = 11.783 is 100%

ln(1024) = 6.931 is 58.824%

in PHP, that function is called log()

no need to set the base, as you are dividing them to find the relative value.

Alex got it, but to generalize for you and PHPize

logPercent = log(x) / log(top) * 100;

If you take the log of your max y value (131072 in your case) and the log of your y value (256), you end up with a height and a y value which is linear in relation to your drawn axis. you can divide them to get a decimal of the height and times by 100 for %:

using log base 2 seen as it gives integers (though any base should be fine).

log(256) / log(131072) = 8/17 = 0.47 = 47%

in php:

(log(256, 2) / log(131072, 2))*100;