Question

Sabendo que log 2=0,301; log 3= 0,477; log 5= 0,699 e log 7=0,845 determine

Log raiz cúbica de 6

Answer 1

$log(\sqrt[3]{6}) = log(\sqrt[3]{2} \times \sqrt[3]{3} ) \\\\ = log(\sqrt[3]{2}) + log(\sqrt[3]{3}) \\\\\ = log(2^{{1 \over 3}}) + log(3^{{1 \over 3}}) \\\\ = {log(2) \over 3} + { log(3) \over 3} \\\\ { 0,301 \over 3} + { 0,477 \over 3} \\\\ = {301 \over 3000 } + {159 \over 1000} \\\\ = {389 \over 1500 } \\\\ \approx {0.2593}$