log(5)*(5^x-4)=1-x (уравнение)

Найду корень уравнения: log(5)*(5^x-4)=1-x

Вы ввели

       / x    \        
log(5)*\5  - 4/ = 1 - x

$$\left(5^{x} - 4\right) \log{\left(5 \right)} = 1 - x$$

Быстрый ответ

        / 1 + log(625)    2   \      / 1 + log(625)\
     - W\5            *log (5)/ + log\5            /
x1 = -----------------------------------------------
                          log(5)                    

$$x_{1} = \frac{- W\left(5^{1 + \log{\left(625 \right)}} \log{\left(5 \right)}^{2}\right) + \log{\left(5^{1 + \log{\left(625 \right)}} \right)}}{\log{\left(5 \right)}}$$

Сумма и произведение корней

сумма

       / 1 + log(625)    2   \      / 1 + log(625)\
    - W\5            *log (5)/ + log\5            /
0 + -----------------------------------------------
                         log(5)                    

$$0 + \frac{- W\left(5^{1 + \log{\left(625 \right)}} \log{\left(5 \right)}^{2}\right) + \log{\left(5^{1 + \log{\left(625 \right)}} \right)}}{\log{\left(5 \right)}}$$

=

   / 1 + log(625)    2   \      / 1 + log(625)\
- W\5            *log (5)/ + log\5            /
-----------------------------------------------
                     log(5)                    

$$\frac{- W\left(5^{1 + \log{\left(625 \right)}} \log{\left(5 \right)}^{2}\right) + \log{\left(5^{1 + \log{\left(625 \right)}} \right)}}{\log{\left(5 \right)}}$$

произведение

     / 1 + log(625)    2   \      / 1 + log(625)\
  - W\5            *log (5)/ + log\5            /
1*-----------------------------------------------
                       log(5)                    

$$1 \frac{- W\left(5^{1 + \log{\left(625 \right)}} \log{\left(5 \right)}^{2}\right) + \log{\left(5^{1 + \log{\left(625 \right)}} \right)}}{\log{\left(5 \right)}}$$

=

   / 1 + log(625)    2   \      / 1 + log(625)\
- W\5            *log (5)/ + log\5            /
-----------------------------------------------
                     log(5)                    

$$\frac{- W\left(5^{1 + \log{\left(625 \right)}} \log{\left(5 \right)}^{2}\right) + \log{\left(5^{1 + \log{\left(625 \right)}} \right)}}{\log{\left(5 \right)}}$$

Численный ответ

x1 = 0.873448630586832

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