power function problem (help is much appreciated!)

Question

find the formula for the power function of the form P(x)=ax^b such that P(9)=20 and P(36)=10.

Answer 1

With the 2 conditions and 3 unknowns, substitution will lead to the following:

20 = a9b and 10 = a36b Taking the logarithm of both sides of the equations leads to

log(20) = log(a) + (b)log(9) and log(10) = log(a) + (b)log(36)

Solving both equations simultaneously, you find that a = 60 and b = -.5

So P(x) = 60/sqrt(x)