solve the equation (1/4)^x = (1/8)^2x-1

Question

solve the equation 3^-x+2=27^x-4

Answer 1

Since 4=2^2 and 8=2^3

(1/2)^2x = (1/2)^(3(2x-1))
2x = 3(2x-1)
2x = 6x-3
4x = 3
x = 3/4

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since 27 = 3^3

3^-x+2=27^x-4
3^-x+2 = 3^3(x-4)
-x+2 = 3(x-4)
-x+2 = 3x-12
14 = 4x
x = 7/2