Question

Sobre mudança de base dos logaritmos!Se logₐₓ a = 4, calcule logₐₓ $\frac{ \sqrt[3]{a} }{ \sqrt{x} }$Gabarito: $\frac{17}{6}$

Answer 1

logₐₓᵃ = 4 => logₐᵃ/logₐᵃˣ = 4 => 1/(logₐᵃ + logₐˣ) = 4 => 4(1 + logₐˣ) = 1
=> 4 + 4logₐˣ = 1 => 4logₐˣ = -3/4 => logₐˣ = -3/4

logₐₓ (∛a/√x ) = logₐₓᵃ¹/³ - logₐₓˣ¹/²= 1/3logₐₓᵃ - 1/2logₐₓˣ = 1/3.4 -1/2(logₐˣ/ logₐᵃˣ) =
4/3 - 1/2[logₐˣ /(logₐᵃ + logₐˣ) ] = 4/3 -1/2[-3/4 : (1 - 3/4 ) = 4/3 -1/2.(-3/4 :1/4) = 4/3 - 1/2(-3/4. 4) = 4/3 - (1/2).3 = 4/3 + 3/2 = (8 + 9)/6 = 17/6