3^(x^2-4)=5^(2*x) (уравнение)

Найду корень уравнения: 3^(x^2-4)=5^(2*x)

Вы ввели

  2           
 x  - 4    2*x
3       = 5   

$$3^{x^{2} - 4} = 5^{2 x}$$

Сумма и произведение корней

сумма

         _____________________               _____________________         
        /    2           2                  /    2           2             
    - \/  log (5) + 4*log (3)  + log(5)   \/  log (5) + 4*log (3)  + log(5)
0 + ----------------------------------- + ---------------------------------
                   log(3)                               log(3)             

$$\left(\frac{- \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}} + \log{\left(5 \right)}}{\log{\left(3 \right)}} + 0\right) + \frac{\log{\left(5 \right)} + \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}}}{\log{\left(3 \right)}}$$

=

   _____________________                 _____________________         
  /    2           2                    /    2           2             
\/  log (5) + 4*log (3)  + log(5)   - \/  log (5) + 4*log (3)  + log(5)
--------------------------------- + -----------------------------------
              log(3)                               log(3)              

$$\frac{- \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}} + \log{\left(5 \right)}}{\log{\left(3 \right)}} + \frac{\log{\left(5 \right)} + \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}}}{\log{\left(3 \right)}}$$

произведение

       _____________________             _____________________         
      /    2           2                /    2           2             
  - \/  log (5) + 4*log (3)  + log(5) \/  log (5) + 4*log (3)  + log(5)
1*-----------------------------------*---------------------------------
                 log(3)                             log(3)             

$$1 \frac{- \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}} + \log{\left(5 \right)}}{\log{\left(3 \right)}} \frac{\log{\left(5 \right)} + \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}}}{\log{\left(3 \right)}}$$

=

-4

$$-4$$

Быстрый ответ

          _____________________         
         /    2           2             
     - \/  log (5) + 4*log (3)  + log(5)
x1 = -----------------------------------
                    log(3)              

$$x_{1} = \frac{- \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}} + \log{\left(5 \right)}}{\log{\left(3 \right)}}$$

        _____________________         
       /    2           2             
     \/  log (5) + 4*log (3)  + log(5)
x2 = ---------------------------------
                   log(3)             

$$x_{2} = \frac{\log{\left(5 \right)} + \sqrt{\log{\left(5 \right)}^{2} + 4 \log{\left(3 \right)}^{2}}}{\log{\left(3 \right)}}$$

Численный ответ

x1 = 3.94411599673754

x2 = -1.01416895530169

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