Question

Log_2(x)^2-log_2(x^2)-3=0

Answer 1

Пошаговое объяснение:

$></p> <p><em>ОДЗ: x>0.</em></p> <p>Пусть log₂x=t      ⇒</p> <p><img src=$

Ответ: x₁=8    x₂=1/2.

Answer 2

To solve the equation $\log_2(x)^2 - \log_2(x^2) - 3 = 0$, let's break down the steps:

Step 1: Rewrite the equation using logarithm properties.

• Using the logarithm property $\log_a(b^c) = c \cdot \log_a(b)$, we can simplify the equation: $2 \cdot \log_2(x) - 2 \cdot \log_2(x) - 3 = 0$

Step 2: Simplify the equation.

• Since the two terms with $\log_2(x)$ cancel out, the equation becomes: $-3 = 0$

Step 3: Analyze the result.

• The equation $-3 = 0$ is not true for any value of $x$. This means that there is no real solution to the original equation $\log_2(x)^2 - \log_2(x^2) - 3 = 0$.

Therefore, the original equation has no real solutions. It's possible that there was a mistake in the equation or in the way it was presented. If you have any additional context or information, please provide it, and I'd be happy to help further.