Logs logs logs help!?

Question

Solve: 4(log(base2)x)^4 – 7(log(base2)x)^2 +3(log(base2)x) = 0

Answer

Let log(base2)x = y. Then your equation becomes the quartic :
4y^4 – 7y^2 + 3y = 0
y ( 4y^3 – 7y + 3 ) = 0
y ( y -1 ) ( 4y^2 + 4y – 3 ) = 0
y ( y -1 ) ( 2y + 3 ) ( 2y – 1 ) = 0

So,

y = 0 , 1 , (- 3/2), or (1/2)

Hence since x = 2^y,

x = 2^0 , 2^1, 2^(-3/2) or 2^(1/2)

equivalently,

x = 1, 2, 2^(-3/2) or √2.