Question

sabendo que o valor de log2 é 0,301 e log5= 0,69,calcule o valor do.log da imagem​

Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf \sqrt[c]{a^b}=a^{\frac{b}{c}}$

• $\sf log_{b}~a^n=n\cdot log_{b}~a$

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

Temos:

$\sf log~\sqrt[4]{20}=log~20^{\frac{1}{4}}$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot log~20$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot log~(2^2\cdot5)$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot(log~2^2+log~5)$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot(2\cdot log~2+log~5)$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot(2\cdot0,301+0,699)$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot(0,602+0,699)$

$\sf log~\sqrt[4]{20}=\dfrac{1}{4}\cdot1,301$

$\sf log~\sqrt[4]{20}=\dfrac{1,301}{4}$

$\sf \red{log~\sqrt[4]{20}=0,325}$