Exponential Function HELP!

[paohabla]

Hi I am from Puerto Rico, and I was taking a Calculus test and suddenly I found a verbal problem that didn't understand. I know I have to deal with logarithms but do not know too much how to use them correctly. So if anyone could help me I would be so grateful...

The verbal problem is:

If there are initially 6000 chickens and this increases exponentially in such a manner that there are 3 times as many chickens after 20 years, then the following is the number of chickens after 11 years.

y=6000*(3)^x/20

[asha]

Can you help with this equation?


log L = 647.98 - 57.13*log R + 188.50*log G - 250.04*log B - 0.65*log t + 2.68*log R^2 -8.63*log G^2 + 11.40*log B^2 + 0.02*log t^2

I tried to simplify it in the following manner:

=> log L = 647.98 - 57.13*log R + 188.50*log G - 250.04*log B - 0.65*log t + 2.68(2log R) -8.63(2log G) + 11.40(2log B) + 0.02(2log t) [as, log b(m^n) = n .log b(m) ]
=> log L = 647.98 - 57.13*log R + 188.50*log G - 250.04*log B - 0.65*log t + 5.36log R -17.26log G + 22.8log B + 0.04log t
=> log L = 647.98 + (5.36 - 57.13)log R + (188.50 - 17.26)log G + (22.8 - 250.04)log B + (0.04 - 0.65)log t
=> log L = 647.98 - 51.77log R + 171.24log G – 227.24log B – 0.61log t
=> L = exp (647.98 - 51.77log R + 171.24log G – 227.24log B – 0.61log t) [if, log e y=x then, ex = y ]
=> L = exp (647.98 - 51.77log R + 171.24log G – 227.24log B – 0.61log t)
=> L = {exp(647.98) . exp(171.24log G)} / {exp(227.24log B) . exp(0.61log t) . exp(51.77log R)} [as, exp(x1) • exp(x2) = exp(x1+x2)]
=> L = {exp(647.98) . exp(171.24) . G} / {exp(227.24) . B . exp(0.61) . t . exp(51.77) . R} [as, exp(log n x) = x]

Can it be simplified further. e.g. L=a*R+b*G+c*B+d*t