Для решения данной задачи воспользуемся свойствами логарифмов:
log2 5^4 log2 3^4 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = a^4 b^4
Поэтому log16 45 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = log2 5^4 log2 3^4 = log2^4 45 = log16 45 = (2log2 5) (4log2 3) = 8log2 5 + 16log2 3 = 8a + 16b
Для решения данной задачи воспользуемся свойствами логарифмов:
log16 45 = log2^4 45 = log2^(log2 16) 45 = log2(45)^4 = log2(53)^4 = log2 5^4 log2 3^4Подставим значение a и b в последнее выражение:log2 5^4 log2 3^4 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = a^4 b^4
Поэтому log16 45 = a^4 b^4 = (log2 5)^4 (log2 3)^4 = log2 5^4 log2 3^4 = log2^4 45 = log16 45 = (2log2 5) (4log2 3) = 8log2 5 + 16log2 3 = 8a + 16b