Question

Questão sobre logarítmos

Answer 1

Boa tarde Aluna!

Solução!

Para resolver o exercicio precisa lembrar das propriedades dos logaritmos.


$log \sqrt[5]{ \dfrac{6000\times0,64}{216} }\\\\\\\\\ log4=0,60206\\\\\\\ log6=0,77815$


$log\bigg( \dfrac{6000\times 0,64}{216}\bigg)^{ \dfrac{1}{5} }\\\\\\\\\ \dfrac{1}{5} log\bigg( \dfrac{6000\times 0,64}{216}\bigg)\\\\\\\\\\\ \dfrac{1}{5}\bigg(log6.1000+ log\frac{64}{100}-log216\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(log6+log1000+log64-log100-log216\bigg)$



$Lembrando!\\\\\\\ 216=6^{3}\\\\\\ 1000=10^{3}\\\\\\ 100=10^{2}\\\\\log_{10}10=1\\\\\\\ 64=2^{4}$



$\dfrac{1}{5}\bigg(log6+log10^{3} +64-log10^{2} -log6^{3} \bigg)\\\\\\\\ \dfrac{1}{5}\bigg(log6+3log10 +3log4-2log10 -3log6\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(log6+3.1 +4log2-2.1 -3log6\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(log6+3 +4log2-2 -3log6\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(0,77815+3 +4(0,60206)-2 -3(0,77815)\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(0,77815+3 +2,40824-2 -2,33445\bigg)\\\\\\\\ \dfrac{1}{5}\bigg(1,85194\bigg)\\\\\\\\ \bigg( \dfrac{1,85194}{5} \bigg)=0,370388$



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Bons estudos!