Произведение корней 3^(3*x-4)/(3^((-5)*x+2))=27

Сумма и произведение корней

сумма

9   log(19683)     pi*I     log(19683)     pi*I     log(19683)     pi*I     log(19683)     pi*I     9    3*pi*I    9    3*pi*I    9    pi*I 
- + ---------- - -------- + ---------- - -------- + ---------- + -------- + ---------- + -------- + - - -------- + - + -------- + - + ------
8    8*log(3)    2*log(3)    8*log(3)    4*log(3)    8*log(3)    4*log(3)    8*log(3)    2*log(3)   8   4*log(3)   8   4*log(3)   8   log(3)

$$\left(\left(\left(\frac{9}{8} - \frac{3 i \pi}{4 \log{\left(3 \right)}}\right) + \left(\left(\left(\left(\frac{9}{8} + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}}\right)\right)\right) + \left(\frac{9}{8} + \frac{3 i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{9}{8} + \frac{i \pi}{\log{\left(3 \right)}}\right)$$

=

9   log(19683)    pi*I 
- + ---------- + ------
2    2*log(3)    log(3)

$$\frac{9}{2} + \frac{\log{\left(19683 \right)}}{2 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}$$

произведение

  /log(19683)     pi*I  \                                                                                                                   
9*|---------- - --------|                                                                                                                   
  \ 8*log(3)    2*log(3)/ /log(19683)     pi*I  \ /log(19683)     pi*I  \ /log(19683)     pi*I  \ /9    3*pi*I \ /9    3*pi*I \ /9    pi*I \
-------------------------*|---------- - --------|*|---------- + --------|*|---------- + --------|*|- - --------|*|- + --------|*|- + ------|
            8             \ 8*log(3)    4*log(3)/ \ 8*log(3)    4*log(3)/ \ 8*log(3)    2*log(3)/ \8   4*log(3)/ \8   4*log(3)/ \8   log(3)/

$$\frac{9 \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}}\right)}{8} \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{4 \log{\left(3 \right)}}\right) \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{4 \log{\left(3 \right)}}\right) \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}}\right) \left(\frac{9}{8} - \frac{3 i \pi}{4 \log{\left(3 \right)}}\right) \left(\frac{9}{8} + \frac{3 i \pi}{4 \log{\left(3 \right)}}\right) \left(\frac{9}{8} + \frac{i \pi}{\log{\left(3 \right)}}\right)$$

=

81*(-4*pi*I + log(19683))*(-2*pi*I + log(27))*(-2*pi*I + log(19683))*(2*pi*I + log(27))*(2*pi*I + log(19683))*(4*pi*I + log(19683))*(8*pi*I + log(19683))
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                                                                                 7                                                                       
                                                                     16777216*log (3)                                                                    

$$\frac{81 \left(\log{\left(27 \right)} - 2 i \pi\right) \left(\log{\left(27 \right)} + 2 i \pi\right) \left(\log{\left(19683 \right)} - 4 i \pi\right) \left(\log{\left(19683 \right)} - 2 i \pi\right) \left(\log{\left(19683 \right)} + 2 i \pi\right) \left(\log{\left(19683 \right)} + 4 i \pi\right) \left(\log{\left(19683 \right)} + 8 i \pi\right)}{16777216 \log{\left(3 \right)}^{7}}$$