Question

Найти значение выражения (логарифмы). Задание № 5

Answer 1

log(a) b = 1/log(b) a

a ^ log(a) b = b

log(a) b^k = k log(a) b

a^m*a^n = a^(m+n)

-------------------------

1/log(2)3 = log(3) 2

1/log(4) 3 = log(3) 4 = log(3) 2^2

.............................

1/log(256) 3 = log(3) 256 = log(3) 2^8

⁹√( 3^(log(3) 2)*3^(log(3) 2^2)*3^(log(3) 2^3)*....*3^(log(3) 2^8)) =

= ⁹√(2*2^2*2^3*2^4*2^5*2^6*2^7*2^8) = ⁹√(2^(1+2+3+4+5+6+7+8) =

= ⁹√ 2^36 = ⁹√ (2^4)^9 = 2^4 = 16