3^x=4-x (уравнение)

Найду корень уравнения: 3^x=4-x

Вы ввели

 x        
3  = 4 - x

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

Быстрый ответ

x1 = 1

$$x_{1} = 1$$

     -W(log(443426488243037769948249630619149892803)) + log(81)
x2 = ----------------------------------------------------------
                               log(3)                          

$$x_{2} = \frac{- W\left(\log{\left(443426488243037769948249630619149892803 \right)}\right) + \log{\left(81 \right)}}{\log{\left(3 \right)}}$$

Сумма и произведение корней

сумма

        -W(log(443426488243037769948249630619149892803)) + log(81)
0 + 1 + ----------------------------------------------------------
                                  log(3)                          

$$\left(0 + 1\right) + \frac{- W\left(\log{\left(443426488243037769948249630619149892803 \right)}\right) + \log{\left(81 \right)}}{\log{\left(3 \right)}}$$

=

    -W(log(443426488243037769948249630619149892803)) + log(81)
1 + ----------------------------------------------------------
                              log(3)                          

$$1 + \frac{- W\left(\log{\left(443426488243037769948249630619149892803 \right)}\right) + \log{\left(81 \right)}}{\log{\left(3 \right)}}$$

произведение

    -W(log(443426488243037769948249630619149892803)) + log(81)
1*1*----------------------------------------------------------
                              log(3)                          

$$1 \cdot 1 \frac{- W\left(\log{\left(443426488243037769948249630619149892803 \right)}\right) + \log{\left(81 \right)}}{\log{\left(3 \right)}}$$

=

-W(log(443426488243037769948249630619149892803)) + log(81)
----------------------------------------------------------
                          log(3)                          

$$\frac{- W\left(\log{\left(443426488243037769948249630619149892803 \right)}\right) + \log{\left(81 \right)}}{\log{\left(3 \right)}}$$

Численный ответ

x1 = 1.0

x2 = 0.999999999999998

x3 = 1.0

x4 = 0.999999999999929

x5 = 0.999999999999993

x6 = 0.999999999999812

x7 = 1.0

x8 = 0.999999999999976

График