Question

( log₂ x) ^2 - 4log₂ x+3=0

Answer 1

Log(2)x=t   ОДЗ x>0
t^2-4t+3=0
D=16-12=4
t1=(4+2)/2=3; log(2)x=3; x=2^3=8
t2=(4-2)/2=1; log(2)x=1; x=2
Ответ x={2;8}

Answer 2

To solve the equation (log₂x)² - 4log₂x + 3 = 0, we can use substitution to simplify it. Let's make a substitution: let y = log₂x. Now the equation becomes a quadratic equation in terms of y:

y² - 4y + 3 = 0

To solve this quadratic equation, we can factor it:

(y - 3)(y - 1) = 0

Now we have two possible values for y:

1. y - 3 = 0 => y = 3
2. y - 1 = 0 => y = 1

Remember, y = log₂x, so we can now translate these solutions back to x:

1. log₂x = 3
2. log₂x = 1

Now, solve for x:

1. log₂x = 3 Rewrite in exponential form: x = 2³ x = 8

2. log₂x = 1 Rewrite in exponential form: x = 2¹ x = 2

So, the solutions to the original equation are x = 8 and x = 2.