Answer to Question #222479 in Algebra for Chrissy

Question

4^x-9*2^x+8 =0

Answer 1

4^x = (2^x)²;

Let 2^x = y;

y² - 9y + 8 = 0

Discriminant = 81 - 32 = 49;

$y_1 = \frac{9 + \sqrt{49}}{2} = 8; y_2 = \frac{9 - \sqrt{49}}{2} = 1;$

Now lets solve it for x using y₁ and y_2;

For y₁ =8 :

$2^x = 8 \\ x_1 = 3;$

For y₂ = 1:

$2^x = 1; \\ x_2 = 0;$

Answer: x₁ = 3, x₂ = 0.