Answer:
t = 2 and t = 3.
Explanation:
To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:
2^t = 4Taking the logarithm base 2 of both sides:
t = log2(4)
t = 2For u = 8:
2^t = 8Taking the logarithm base 2 of both sides:
t = log2(8)
t = 3