Question

AAJUDEEMM Sabendo que log 2=0,3 calcule o valor de: log raiz quinta de 125???​

Answer 1

Explicação passo-a-passo:

Lembre-se que:

$\sf log_{b}~\Big(\dfrac{a}{c}\Big)=log_{b}~a-log_{b}~c$

Assim:

$\sf log~5=log~\Big(\dfrac{10}{2}\Big)$

$\sf log~5=log~10-log~2$

$\sf log~5=1-0,3$

$\sf log~5=0,7$

Lembre-se que:

• $\sf log_{b}~a^m=m\cdot log_{b}~a$

• $\sf \sqrt[c]{a^b}=a^{\frac{b}{c}}$

Logo:

$\sf log~\sqrt[5]{125}=log~\sqrt[5]{5^3}$

$\sf log~\sqrt[5]{125}=log~5^{\frac{3}{5}}$

$\sf log~\sqrt[5]{125}=\dfrac{3}{5}\cdot log~5$

$\sf log~\sqrt[5]{125}=\dfrac{3}{5}\cdot0,7$

$\sf log~\sqrt[5]{125}=\dfrac{2,1}{5}$

$\sf \red{log~\sqrt[5]{125}=0,42}$