To solve the first equation 10^x - 8.5^x = 0, we can write it as:

10^x = 8.5^x

Taking the natural log of both sides, we get:

x ln(10) = x ln(8.5)

Dividing by x on both sides (assuming x is not equal to 0), we get:

ln(10) = ln(8.5)

This equation does not have any real solutions, as ln(10) is not equal to ln(8.5).

Moving on to the second equation 16^x - 12*4^x - 64 = 0, we can factor this expression as:

(4^x - 8)(4^x - 4) = 0

This gives us two equations:

1) 4^x - 8 = 0
4^x = 8
x = log(8)/log(4)
x = 3/2

2) 4^x - 4 = 0
4^x = 4
x = log(4)/log(4)
x = 1

Therefore, the solutions to the second equation 16^x - 12*4^x - 64 = 0 are x = 3/2 and x = 1.