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

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    Решение

    Сумма и произведение корней [src]
    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)
    (((983iπ4log(3))+((((98+(log(19683)8log(3)iπ2log(3)))+(log(19683)8log(3)iπ4log(3)))+(log(19683)8log(3)+iπ4log(3)))+(log(19683)8log(3)+iπ2log(3))))+(98+3iπ4log(3)))+(98+iπlog(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)
    92+log(19683)2log(3)+iπlog(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)/
    9(log(19683)8log(3)iπ2log(3))8(log(19683)8log(3)iπ4log(3))(log(19683)8log(3)+iπ4log(3))(log(19683)8log(3)+iπ2log(3))(983iπ4log(3))(98+3iπ4log(3))(98+iπlog(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))
    ---------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     7                                                                       
                                                                         16777216*log (3)                                                                    
    81(log(27)2iπ)(log(27)+2iπ)(log(19683)4iπ)(log(19683)2iπ)(log(19683)+2iπ)(log(19683)+4iπ)(log(19683)+8iπ)16777216log(3)7\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}}