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