Question

solve
${4}^{x} - 5 \times {2}^{x} + 4 = 0$
​

Answer 1

Answer:

0 or 2

Step-by-step explanation:

Given :

4ˣ - 5 × 2ˣ + 4 = 0

2ˣ × 2ˣ - 5 × 2ˣ + 4 = 0

Let 2ˣ = y

y² - 5 y + 4 = 0

y² - 4 y - y + 4 = 0

y ( y - 4 ) - ( y - 4 ) = 0

( y - 1 ) ( y - 4 ) = 0

y - 1 = 0

y = 1

OR

y - 4 = 0

y = 4

Now on comparing :

2ˣ = 4

2ˣ = 2²

x = 2

OR

2ˣ = 1

2ˣ = 2⁰

x = 0

Therefore , the value of x is 0 OR 2 .