Вычислите: 25¹/log₆5 + 49¹/log₈7

Используем свойство: x¹/log<0xE1><0xB5><0xA7>x = y.

25¹/log₆5 = 25^(log₅6) = (5²) ^ (log₅6) = 5^(2 * log₅6) = 5^(log₅6²) = 6².

49¹/log₈7 = 49^(log₇8) = (7²) ^ (log₇8) = 7^(2 * log₇8) = 7^(log₇8²) = 8².

Таким образом, 6² + 8² = 36 + 64 = 100.