3^x-x+5=0 (уравнение)

Найду корень уравнения: 3^x-x+5=0

Вы ввели

 x            
3  - x + 5 = 0

$$3^{x} - x + 5 = 0$$

Быстрый ответ

     -re(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) + log(243)   I*im(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627)))
x1 = --------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------
                                                                         log(3)                                                                                                                                     log(3)                                                              

$$x_{1} = \frac{- \operatorname{re}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)} + \log{\left(243 \right)}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)}}{\log{\left(3 \right)}}$$

Сумма и произведение корней

сумма

    -re(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) + log(243)   I*im(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627)))
0 + --------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------
                                                                        log(3)                                                                                                                                     log(3)                                                              

$$0 + \left(\frac{- \operatorname{re}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)} + \log{\left(243 \right)}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)}}{\log{\left(3 \right)}}\right)$$

=

-re(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) + log(243)   I*im(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627)))
--------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------
                                                                    log(3)                                                                                                                                     log(3)                                                              

$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)} + \log{\left(243 \right)}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)}}{\log{\left(3 \right)}}$$

произведение

  /-re(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) + log(243)   I*im(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627)))\
1*|--------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------|
  \                                                                    log(3)                                                                                                                                     log(3)                                                              /

$$1 \left(\frac{- \operatorname{re}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)} + \log{\left(243 \right)}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)}}{\log{\left(3 \right)}}\right)$$

=

-re(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) - I*im(W(-log(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627))) + log(243)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                       log(3)                                                                                                                                      

$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)} + \log{\left(243 \right)} - i \operatorname{im}{\left(W\left(- \log{\left(87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665627 \right)}\right)\right)}}{\log{\left(3 \right)}}$$

Численный ответ

x1 = 1.33759966971673 - 2.3417714542238*i

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