Sejam a, b, c e d números reais positivos, tais que blog a 5, blog c 2 e blog d 3. O valor da expressão 2 5 c 3 a blog d é igual a: a) 1 b)...

Podemos utilizar as propriedades dos logaritmos para resolver essa questão. Temos que: blog a 5 = b blog c 2 = 5 blog d 3 = 2 Logo, podemos escrever: a = 5^b c = 2^5 d = 3^2 Substituindo esses valores na expressão 2^(5c) / (3ad), temos: 2^(5c) / (3ad) = 2^(5*2^5) / (3*5^b*3^2) Simplificando, temos: 2^(5c) / (3ad) = 2^(2^3 + 2^2) / (5^b*3^3) 2^(5c) / (3ad) = 2^8 / (5^b*3^3) 2^(5c) / (3ad) = 256 / (5^b*27) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b) 2^(5c) / (3ad) = 256 / (27*5^b) 2^(5c) / (3ad) = 256 / (3^3*5^b)