Question

Qual é o valor da expressão log2 0,5 + log3 $\sqrt{3}$ + log4 8 + $log_{0,1}$ 0,001 + 5 . log3 $\sqrt[5]{27}$ ?

Answer 1

$\log_20,5+\log_3\sqrt{3}+\log_48+\log_{0,1}0,001+5\cdot\log_3\sqrt[5]{27}=\\\\\log_2\frac{1}{2}+\log_33^{\frac{1}{2}}+\log_{2^2}2^3+\log_{0,1}(0,1)^3+5\cdot\log_33^{\frac{3}{5}}=\\\\\log_22^{-1}+\frac{1}{2}+3\cdot\frac{1}{2}+3+5\cdot\frac{3}{5}=\\\\-1+\frac{1}{2}+\frac{3}{2}+3+3=\\\\-1+2+6=\\\\\boxed{7}$