Mister Exam
5log5^(x-y)=1; 3^x-3^y=6log28
The solution
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x - y 5*log (5) = 1
$$5 \log{\left(5 \right)}^{x - y} = 1$$
x y 3 - 3 = 6*log(28)
$$3^{x} - 3^{y} = 6 \log{\left(28 \right)}$$
3^x - 3^y = 6*log(28)
Rapid solution
$$x_{1} = \frac{\log{\left(- \log{\left(28^{\frac{6}{1 - 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
$$\frac{\log{\left(\log{\left(28^{\frac{6}{-1 + 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
$$y_{1} = \frac{\log{\left(\log{\left(481890304^{- \frac{5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}{1 - 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
$$\frac{\log{\left(\log{\left(481890304^{- \frac{5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}{1 - 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
=
$$\frac{\log{\left(\log{\left(28^{\frac{6}{-1 + 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
-0.633031997504619 + 2.85960086738013*i
$$y_{1} = \frac{\log{\left(\log{\left(481890304^{- \frac{5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}{1 - 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
$$\frac{\log{\left(\log{\left(481890304^{- \frac{5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}{1 - 5^{\log{\left(3^{\frac{1}{\log{\left(\log{\left(5 \right)} \right)}}} \right)}}}} \right)} \right)} + i \pi}{\log{\left(3 \right)}}$$
=
2.74895719786351 + 2.85960086738013*i