Solve 8(4^x ) – 9(2^x ) + 1 = 0

At first this equation seems tricky, but we can perform a clever substitution to simplify it. We notice that if let y = 2^x, then we can rewrite this as:

8(y^2) - 9y + 1 = 0

This now becomes a simple quadratic equation, which can be simplified to: (8y -1) (y-1) = 0

Therefore y = 1/8; y =1. Now solving for x: 2^x = 1/8 leads to x = -3; 2^x = 1 leads to x = 0;