Question

Найдите корень уравнения. Решите аж по этапно

Answer 1

$685) 25^{x-11} = \frac15\\5^{2(x-11)} = 5^{-1}\\2(x-11) = -1\\2x - 22 = -1\\2x = 21\\x = \frac{21}2$

$686) 9^{x-1} = \frac13\\3^{2(x-1)} = 3^{-1}\\2(x-1) = -1\\2x-2 = -1\\2x = 1\\x = \frac12$

$687) 25^{x-7} = \frac15\\5^{2(x-7)} = 5^{-1}\\2x - 14 = -1\\2x = 13\\x = \frac{13}2$

$688) (\frac1{16})^{x-9} = 4\\4^{-2(x-9)} = 4^1\\-2(x-9) = 1\\-2x + 18 = 1\\-2x = -17\\x = \frac{17}2$

$689) (\frac1{81})^{x-11} = 3\\3^{-4(x-11)} = 3^1\\-4(x-11) = 1\\-4x + 44 = 1\\-4x = -43\\x = \frac{43}4$

$690) (\frac1{32})^{x-2} = 2\\2^{-5(x-2)} = 2^1\\-5(x-2) = 1\\-5x + 10 = 1\\-5x = -9\\x = \frac95$