Question

sendo log x 2 = a , log x 3 = b calcule log x raiz de 12

Answer 1

Eae,

use as propriedades, do produto e da potência de log..

$\large\boxed {log_b(np)\Rightarrow log_b(n\cdot p)\Rightarrow log_b(n)+log_b(p)}\\\\ \boxed{log_b(p)^n\Rightarrow n\cdot log_b(p)}}$

$log_x \sqrt{12}=log_x( \sqrt[2]{12^1})\\ log_x \sqrt{12}=log_x(12)^{ \tfrac{1}{2} }\\ log_x \sqrt{12} = \dfrac{1}{2}\cdot log_x(12)\\\\ log_x \sqrt{12}= \dfrac{1}{2}\cdot log_x(2^2\cdot3)\\\\ log_x \sqrt{12}= \dfrac{1}{2}\cdot log_x(2)^2+log(3)\\\\ log_x \sqrt{12}=2\cdot \dfrac{1}{2}\cdot log_x(2)+log_x(3)\\\\ log_x \sqrt{12}=log_x(2)+log_x(3)\\\\ \huge\boxed{\boxed{log_x \sqrt{12}=a+b}}$

Tenha ótimos estudos ;D e qualquer dúvida me chame nos comentários..