Desenvolva, aplicando as propriedades dos logaritmos a- log (3.4) = 5b- log (2.3.5.) = 4c - log 2\/3 = 5

\[\eqalign{ & \dfrac{{\log 3 + \log 4}}{{\log 5}} \cr & \dfrac{{\log 3 + \log {2^2}}}{{\log 5}} \cr & \dfrac{{\log 3 + 2\log 2}}{{\log 5}} \cr & \dfrac{{\log 3 + 2log\dfrac{{10}}{5}}}{{\log 5}} \cr & \dfrac{{\log 3 + 2\log 10 - 2\log 5}}{{\log 5}} \cr & \dfrac{{\log 3 + 2 - 2\log 5}}{{\log 5}} }\]

Assim é o máximo que podemos simplificar o cálculo.

Letra B

\[\eqalign{ & \dfrac{{\log 2 + \log 3 + \log 5}}{{\log 4}} \cr & \dfrac{{\log 2 + \log 3 + \log \dfrac{{10}}{2}}}{{\log {2^2}}} \cr & \dfrac{{\log 2 + \log 3 + \log 10 - \log 2}}{{2\log 2}} \cr & \dfrac{{\log 3 + 1}}{{2\log 2}} }\]

Letra C

\[\eqalign{ & \dfrac{{\log (\dfrac{2}{3})}}{{\log 5}} \cr & \dfrac{{\log 2 - \log 3}}{{\log 5}} \cr & \dfrac{{\log \dfrac{{10}}{5} - \log 3}}{{\log 5}} \cr & \dfrac{{\log 10 - \log 5 - \log 3}}{{\log 5}} \cr & \dfrac{{1 - \log 5 - \log 3}}{{\log 5}} }\]

Portanto temos acima os três cálculos resolvidos.