The thread is now closed but I was working on this one problem...the one with eggs that Kadyo posted.
# of eggs doubles every minute, after one hr, the basket is full, when was it half full?
Solve using logarithms and the change of base formula.
2^60 = 1.152921505 X 10^18 (the number of eggs in the basket after one hr)
(1.152921505 X 10^18) X 0.5 = 5.764607523 X 10^17 (the number of eggs in the basket when it is half full)
so 2^x = (5.764607523 X 10^17), x is the time at which the basket is half full
take the log of both sides,
Log base 2(2^x) = Log base 2(5.764607523 X 10^17)
rearranging for x on the left we have,
xLog base 2(2) = Log base 2(5.764607523 X 10^17)
x*(1) = Log base 2(5.764607523 X 10^17)
Using the change of base formula,
x = ln(5.764607523 X 10^17) / ln(2)
x = 59 minutes
The problems in that thread were fun...the other comments were just un-necessary.