2^x*5^y=40 5^x*2^y=250
Решение
Вы ввели
[TeX]
[pretty]
[text]
x y 2 *5 = 40
$$2^{x} 5^{y} = 40$$
x y 5 *2 = 250
$$2^{y} 5^{x} = 250$$
Быстрый ответ
[TeX]
$$x_{1} = \frac{- \log{\left (5 \right )} \log{\left (250 \right )} + \log{\left (2 \right )} \log{\left (40 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
$$\frac{- \log{\left (5 \right )} \log{\left (250 \right )} + \log{\left (2 \right )} \log{\left (40 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
$$y_{1} = \frac{- \log{\left (5 \right )} \log{\left (40 \right )} + \log{\left (2 \right )} \log{\left (250 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
$$\frac{- \log{\left (5 \right )} \log{\left (40 \right )} + \log{\left (2 \right )} \log{\left (250 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
=
$$\frac{- \log{\left (5 \right )} \log{\left (250 \right )} + \log{\left (2 \right )} \log{\left (40 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
3
$$y_{1} = \frac{- \log{\left (5 \right )} \log{\left (40 \right )} + \log{\left (2 \right )} \log{\left (250 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
$$\frac{- \log{\left (5 \right )} \log{\left (40 \right )} + \log{\left (2 \right )} \log{\left (250 \right )}}{- \log^{2}{\left (5 \right )} + \log^{2}{\left (2 \right )}}$$
=
1
Численный ответ
[pretty]
[text]
x1 = 3.00000000000000 y1 = 1.00000000000000
x2 = 2.999999999999997 y2 = 1.000000000000007