Question

10^log100 x^2=2x Help

Answer 1

Ответ:

Если допустить, что написанное Вами условие задания я понял правильно как (10^log100)× х² =2х  , то решение его таково:

1) Прологарифмируем обе части уравнения по основанию 10:

 log[(10^log100)× х²]=log(2x) ⇒ log100·log10+logх²=log(2x) ⇒ 2·1=log(2x/x²)

  ⇒ 10²=2x/x² ⇒ 100=2/x ⇒ 100x=2 ⇒x=0,02

Пошаговое объяснение:

Answer 2

To solve the equation $10^{\log(100)}x^2 = 2x$, we can simplify it step by step.

1. Start by simplifying the expression on the left side using properties of logarithms. The log base 10 of 100 is 2 because $10^2 = 100$:

   $10^{\log(100)} = 10^2 = 100$

2. Substitute this value back into the equation:

   $100x^2 = 2x$

3. Divide both sides of the equation by 2 to isolate $x$:

   $50x^2 = x$

4. Now, move all terms to one side of the equation to set it equal to zero:

   $50x^2 - x = 0$

5. Factor the equation if possible. In this case, you can factor out an $x$:

   $x(50x - 1) = 0$

6. Set each factor equal to zero and solve for $x$:

   $x = 0$ (from $x = 0$)

   $50x - 1 = 0$

7. Solve for $x$ in the second equation:

   $50x = 1$

   $x = \frac{1}{50}$

So, the solutions to the equation $10^{\log(100)}x^2 = 2x$ are $x = 0$ and $x = \frac{1}{50}$.