Question

Dados log 2 = 0,301 ; log 3 = 0,477 ; log 5 = 0,699 e log 7 = 0,845 . Calcule: raiz de 125

Answer 1

Oi Larissa,

no logaritmo $\mathsf{ log \sqrt{125}}$ fatoramos 125 dentro da raiz,

use a propriedade de expoente racional

$\mathsf{ ^n\sqrt{a^m} =a^{ \tfrac{m}{n} } }$

e em seguida a propriedade da potência de log:

$\mathsf{log_b(a)^n=n\cdot log_b(a)}$

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

$\mathsf{log \sqrt{125}=log \sqrt{5^3} }\\ \mathsf{ log \sqrt{125}=log(5^{ \tfrac{3}{2}}) } }\\ \mathsf{ log \sqrt{125}=log(5)^{ \tfrac{3}{2} } }\\\\ \mathsf{ log \sqrt{125}= \dfrac{3}{2} \cdot log5 }\\\\ \mathsf{LEMBRA~QUE~log5, ~vale~0,699,~substiua-o:}\\\\ \mathsf{ log \sqrt{125}= \dfrac{3}{2}\cdot0,699 }\\\\\\ \mathsf{ log \sqrt{125}= \dfrac{3\cdot0,699}{2} }\\\\\\ \mathsf{ log \sqrt{125}= \dfrac{2,097}{2} }\\\\\\ \Large\boxed{\mathsf{ log \sqrt{125}=1,0485}}$

Tenha ótimos estudos ;D