Question

Sabendo que log2=0,3010, determine o valor da expressão log(125/cinco raiz de 2

Answer 1

$\log\left(\dfrac{125}{\sqrt2}\right)=\\\\\log(125)-\log(\sqrt2)=\\\\\log(5^3)-\log(2^{\frac12})=\\\\3\log(5)-\dfrac12\cdot\log(2)=\\\\3\log\left(\dfrac{10}{2}\right)-\dfrac12\cdot\log(2)=\\\\3(\log(10)-\log(2))-\dfrac12\cdot\log(2)=\\\\3(1-0.3010)-\dfrac12\cdot0.3010=\\\\3(0.6990)-0.1505=\\\\2.097-0.1505=1.9465$

Answer 2

Resposta:

R= 2,0368

Explicação passo-a-passo:

(A resposta anterior colocou $log(\frac{125}{\sqrt{2} })$ invés de $log(\frac{125}{\sqrt[5]{2} })$ como solicitado, logo vem dar a resposta certa)

$log(\frac{125}{\sqrt[5]{2} })$

$log(\frac{5^{3} }{2^{\frac{1 }{5 }} })$

$log(5^{3})-log(2^{\frac{1 }{5 } })$

$3*log(5) - \frac{1 }{5 }*log(2)$

$3*log(\frac{10}{2}) - \frac{1 }{5 }*log(2)$

$3*(log(10) - log(2)) - \frac{1 }{5 }*log(2)$        $(log(2) = 0.3010)$

$3*(1 - 0.3010) - \frac{1 }{5 }*0.3010$

$3*(0.699) - \frac{1 }{5 }* 0.3010$

$3 * 0.699 - \frac{1 }{5 } * 0.3010$

$2.097 - 0.0602$

$R= 2.0368$