Произведение корней 3^(3*x-4)/(3^((-5)*x+2))=27
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)
$$\left(\left(\left(\frac{9}{8} - \frac{3 i \pi}{4 \log{\left(3 \right)}}\right) + \left(\left(\left(\left(\frac{9}{8} + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} - \frac{i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(19683 \right)}}{8 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}}\right)\right)\right) + \left(\frac{9}{8} + \frac{3 i \pi}{4 \log{\left(3 \right)}}\right)\right) + \left(\frac{9}{8} + \frac{i \pi}{\log{\left(3 \right)}}\right)$$
=
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)
$$\frac{81 \left(\log{\left(27 \right)} - 2 i \pi\right) \left(\log{\left(27 \right)} + 2 i \pi\right) \left(\log{\left(19683 \right)} - 4 i \pi\right) \left(\log{\left(19683 \right)} - 2 i \pi\right) \left(\log{\left(19683 \right)} + 2 i \pi\right) \left(\log{\left(19683 \right)} + 4 i \pi\right) \left(\log{\left(19683 \right)} + 8 i \pi\right)}{16777216 \log{\left(3 \right)}^{7}}$$