ElectricPavlov

....so the antilog of 9     would be    10^9 = 1 000 000 000  

Slope = rise/ run  or   (y1-y2) / (x1-x2)

for the first two points

slope = (4-3) / (2-6) = - 1/4

for the second and third points we need slope = -1/4 , then solve for c

(3-c) / (6-(-5) ) = -1/4

3-c = -1/4(11)

3-c = -11/4

3+11/4 = c

23/4 = c     or  5 3/4   or  5.75

Hmmmm.... that looks pretty simplified already.... but you COULD do this

according to the rules of logs

Log (xy) = log(x) + log (y)

WolframAlpha says   x = 1.97567824

http://www.wolframalpha.com/input/?i=0.035674%5Ex+%2B+0.096972%5Ex+%2B+e%5E(-x)+%3D3%2F20

Factor the numerator:  (x-2)(x+1)   leads us to BELIEVE that x = 2  and x = -1 are zeroes

  BUT looking at the denominator  x cannot equal 2   (cannot have a value of zero in the denminator)

    so the only zero left is at   x = -1

3kx - 2k = 4 - 6x

3kx = -6x      and   -2k = 4

3k = -6          and     k = -2

  k = -2

My guestimate:

There are  8 c 3 ways to pick the Republicans  =  56 ways

 for each of these 56 ways to pick a Republican there are

   6 c 2 ways to pick the Dims  = 15

56  x  15 = 840 ways

k=-2 is a solution

Angle c is arcsin (3/5)    (remember sin is  opp/hyp)   = 36.87 degrees

Similar here   angle r     =  arcsin (30/40) = 48.59 degrees

b=10  

10^x = 25     take log (base 10) of both sides

   x = log 25= 1.39794