5^(x-1)+5*(1/5)^(x-2)=26

$$5 left(frac{1}{5}right)^{x – 2} + 5^{x – 1} = 26$$

Дано уравнение:
$$5 left(frac{1}{5}right)^{x – 2} + 5^{x – 1} = 26$$
или
$$5 left(frac{1}{5}right)^{x – 2} + 5^{x – 1} – 26 = 0$$
Сделаем замену
$$v = left(frac{1}{5}right)^{x}$$
получим
$$5 cdot 5^{2} v^{1} – 26 + frac{1}{5 v} = 0$$
или
$$125 v – 26 + frac{1}{5 v} = 0$$
делаем обратную замену
$$left(frac{1}{5}right)^{x} = v$$
или
$$x = – frac{log{left (v right )}}{log{left (5 right )}}$$
Тогда, окончательный ответ
$$x_{1} = frac{log{left (1 right )}}{log{left (frac{1}{5} right )}} = 0$$
$$x_{2} = frac{log{left (3 right )}}{log{left (frac{1}{5} right )}} = – frac{log{left (3 right )}}{log{left (5 right )}}$$

$$x_{1} = 1$$

x2 = 3

$$x_{2} = 3$$

x1 = 1.00000000000000

x2 = 3.00000000000000