Question

Log ² 2 x - log ² x - 3 =0.​

Answer 1

Если нужно разборное решение тогда скину

Answer 2

To solve the equation $\log^2(2x) - \log^2(x) - 3 = 0$, you can use some logarithmic properties to simplify it. Here are the steps to solve it:

1. Apply the properties of logarithms:
   • $\log^2(2x) = 2\log(2x)$
   • $\log^2(x) = (\log(x))^2$

So, the equation becomes:

$2\log(2x) - (\log(x))^2 - 3 = 0$

2. Move the $(\log(x))^2$ term to the left side:

$2\log(2x) - 3 = (\log(x))^2$

3. Take the square root of both sides:

$\sqrt{2\log(2x) - 3} = \log(x)$

4. Eliminate the logarithm by exponentiating both sides:

$x = 10^{\sqrt{2\log(2x) - 3}}$

Now, you have an equation in terms of $x$, but it's not a simple equation to solve algebraically. You might need to use numerical methods or a calculator to find an approximate solution for $x$.