math - Logarithmic distribution -

first of all, math not area.

imagine problem this:

i have number of money spend, 500, , need spend them on fixed number of days, 20. have fixed maximum of money spend per day, 50. don't need spend money on day.

now need know how calculate total number of money have spend each day spending curve following:

my goal function takes number of money , number of days, , returns tuple day number , ammount of money day.

i know need use logarithms of type, , i've tried pretty brain can handle. i've been looking @ wolfram mathworld , formula:

y = + b ln x

but not me.

an hint or example in php, python or c# great, language do.

please let me know if need more information or if question vague, want solve this. thank you!

i don't understand why want log distribution. parabolic 1 obtain curve form want:

 spend[day] = day^2 + c  

where:

a -> (6 * (td - ta)) / (td *(-1 - 3 * td + 4 * td^2))     c -> -((1 + 3 * td - 6*ta*td + 2 * td^2)/ (-1 - 3 * td + 4 * td^2))    ta = total amount td = total days 

with amount spend last day 1.

for example values: (amt 500, days 20)