Question

Solve the following equation:

2^2x – 5.2^x + 4 = 0

Answer 1

Given the equation: 2^2x – 5.2^x + 4 = 0

Step-wise calculation:

1. Let y = 2^x. Then, 2^2x = (2^x)² = y²

2. Substitute in the equation: y² – 5y + 4 = 0

3. Factorize the quadratic: (y – 4)(y – 1) = 0

4. So, y = 4 or y = 1

5. Recall (y = 2^x), solve for (x): 

2^x = 4 

⇒ 2^x = 2² 

⇒ x = 2

2^x = 1 

⇒ 2^x = 2⁰ 

⇒ x = 0