Question

(En) log de raiz de 2 na base 0.125 + log 0.001 na base 0.1 + log raiz de quinta de 27 na base 3 ? Com a solução por favor

Answer 1

Resposta:

103/30

Explicação passo-a-passo:

$log_{0.125}( \sqrt{2} ) + log_{0.1}(0.001) + log_{3}( \sqrt[5]{27} ) \\ log_{0.125}( {2}^{ \frac{1}{2} } ) + log_{0.1}( \frac{1}{1000} ) + log_{3}( {27}^{ \frac{1}{5} } ) \\ \frac{1}{2} . log_{0.125}(2) + log_{0.1}(1) - log_{0.1}(1000) + \frac{1}{5} . log_{3}(27) \\ \frac{1}{2} . log_{ \frac{125}{1000} }(2) + log_{ \frac{1}{10} }(1) - log_{ \frac{1}{10} }( {10}^{3} ) + \frac{1}{5} .3 \\ \frac{1}{2} . log_{ \frac{1}{8} }(2) + 0 - 3. log_{ \frac{1}{10} }(10) + \frac{3}{5} \\ \frac{1}{2} .( - \frac{1}{3} ) - 3.( - 1) + \frac{3}{5} \\ - \frac{1}{6} + 3 + \frac{3}{5} \\ \frac{5 \times ( - 1) + 30 \times 3 + 6 \times 3}{30} \\ \frac{ - 5 + 90 + 18}{30} \\ \frac{103}{30}$