Determine the equation of the inverse of y =4^(2x+9)

Y = 1/2[(logx/log 4) - 9] is the inverse. 

You can solve this by switching the x and y values and then solve. You'll need to use logarithmic functions in order to get the exponents down. 

x =4^(2y+9)---> take logs of both sides and move exponents
logx = (2y + 9)log 4 ---> divide by log4
logx/log4 = 2y + 9 ---> subtract 9
(logx/log4) - 9 = 2y ---> multiply by 1/2
1/2[(logx/log4) - 9] = y