Find the exact solutions of the following equations:

1.

2^(x-3) = (4) 8^(x-2)

2.

3^(2x) + (5) 3^x = 6

2^(x-3) = (4) 8^(x-2)

2^(x-3) = (2^2)*(2^3)^(x-2)

2^(x-3) = (2^2)*[2^(3*(x-2)]

2^(x-3) = (2^2)*[2^(3x-6)]

2^(x-3) = 2^(3x-6+2)

2^(x-3) = 2^(3x-6+2)

2^(x-3) = 2^(3x-4)

x-3 = 3x-4

3x-x = -3+4

2x = 1

x = 1/2