(y-5)^48 = 96^32(y-5) = 96^(32/48)(y-5) = 96^(2/3)(y-5) = (4^2)^(2/3)(y-5) = 4^(2*2/3)(y-5) = 4^(4/3)(y-5) = 4^1.33
Now, we need to solve for y:
(y-5) = 5.278y = 10.278
Therefore, the solution to the equation (y-5)^48 = 96^32 is y = 10.278.
(y-5)^48 = 96^32
(y-5) = 96^(32/48)
(y-5) = 96^(2/3)
(y-5) = (4^2)^(2/3)
(y-5) = 4^(2*2/3)
(y-5) = 4^(4/3)
(y-5) = 4^1.33
Now, we need to solve for y:
(y-5) = 5.278
y = 10.278
Therefore, the solution to the equation (y-5)^48 = 96^32 is y = 10.278.