write the square root of 32as a power of 2 and hence solve the equation 16to the power of x-1=2 square root of 32

Answer 1

since 32 = 2^5,

sqrt(32) = 32^(1/2) = (2^5)^(1/2) = 2^(5/2)

16^(x-1) = 2 * 2^(5/2) = 2^(1 + 5/2) = 2^(7/2)

16 = 2^4

2^(4x-4) = 2^(7/2)
so,
4x-4 = 7/2
8x-8 = 7
8x = 15
x = 15/8