25^{y} - 2 * 5^{y+1}=12500

25^y - 2 * 5^y+1 = 12500,

5^{2 у} - 2 * 5^y * 5 = 12500,

5^{2 у} - 10 * 5^y = 12500,

5^{2 у} - 10 * 5^y - 12500 = 0,

5^y = х, тогда:

х² - 10 * х - 12500 = 0,

D = 50100,

х₁ = (10 + 10√501) / 2 = 5 + 5√501,

х₂ = (10 - 10√501) / 2 = 5 - 5√501,

1) 5^y = 5 + 5√501,

у = log ₅ (5 + 5√501),

у = log ₅ (5 * (1 + √501)),

у = log ₅ 5 + log ₅ (1 + √501),

у = 1 + log ₅ (1 + √501),

2) 5^y = 5 - 5√501,

у = log ₅ (5 - 5√501),

у = log ₅ (5 * (1 - √501)),

у = log ₅ 5 - log ₅ (1 - √501),

у = 1 - log ₅ (1 + √501).