Question

Sendo Logx 2= a , Logx 3 = b calcule logx raiz cúbica de 12.
Me ajudem por favor!!

Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf log_{b}~(a\cdot c)=log_{b}~a+log_{b}~c$

• $\sf log_{b}~a^m=m\cdot log_{b}~a$

• $\sf \sqrt[c]{a^b}=a^{\frac{b}{c}}$

Assim:

$\sf log_{x}~\sqrt[3]{12}=log_{x}~\sqrt[3]{2^2\cdot3}$

$\sf log_{x}~\sqrt[3]{12}=log_{x}~(2^2\cdot3)^{\frac{1}{3}}$

$\sf log_{x}~\sqrt[3]{12}=\dfrac{1}{3}\cdot log_{x}~(2^2\cdot3)$

$\sf log_{x}~\sqrt[3]{12}=\dfrac{1}{3}\cdot(log_{x}~2^2+log_{x}~3)$

$\sf log_{x}~\sqrt[3]{12}=\dfrac{1}{3}\cdot(2\cdot log_{x}~2+log_{x}~3)$

$\sf log_{x}~\sqrt[3]{12}=\dfrac{1}{3}\cdot(2\cdot a+b)$

$\sf \red{log_{x}~\sqrt[3]{12}=\dfrac{2a+b}{3}}$