Solve the following equation for x:
2^{2x + 1} - 9 \times 2^x + 4 = 0
SOLUTION: This is a quadratic in 2^x.
2 (2^x)^2 - 9 (2^x) +4 = 0
Use a substitution u=2^x and express the equation in terms of u.
Therefore:
2u^2 - 9u +4 = 0
Factorise to get
( 2u- 1 )( u - 4 ) = 0
2u - 1 = 0 or u - 4 = 0
2u = 1 or u = 4
u = 1/2 or u=2^2
2^x=2^{-1} or 2^x=2^2
\therefore x=-1, 2
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