Solve the following equations: $2^{2x + 8} + 1 = 32 . 2^{x}$.

Using the laws of exponents, rewrite 2^(2x + 8) as 2^(2x) * 2^8, which equals 256 * (2^x)^2. Substituting t = 2^x transforms the equation into 256t^2 + 1 = 32t, which rearranges to the quadratic equation 256t^2 - 32t + 1 = 0. Factoring this gives (16t - 1)^2 = 0, meaning t = 1/16. Setting 2^x = 1/16 gives x = -4.

• Thanks
• Wrong explanation