Question

(1/4)^х-3*(1/2)^х+2=0

Answer 1

1/4x-3/2x+2=0
x-6x+8=0
-5x+8=0
-5x=-8
x=8/5

Answer 2

To solve the equation:

(1/4)^x-3*(1/2)^x+2=0

Let's first make a substitution to simplify the equation. Let y = (1/2)^x. Then, we can rewrite the equation as:

y^2 - 3y + 2 = 0

This is a quadratic equation that can be factored as:

(y - 2)(y - 1) = 0

So, y = 2 or y = 1.

Substituting back for y, we get:

(1/2)^x = 2 or (1/2)^x = 1

For the first equation, we take the logarithm of both sides to get:

x log(1/2) = log 2

Solving for x, we get:

x = log 2 / log(1/2)

Using the change of base formula, we can rewrite this as:

x = log 2 / (-log 2)

x = -1

For the second equation, we have:

(1/2)^x = 1

This is only possible if x = 0.

Therefore, the solutions to the original equation are:

x = -1 or x = 0.