Question

Log de raiz de 2 na base 2 + log de 0,09 na base 3 + log de 256 na base 4

Answer 1

$log_{2}( \sqrt{2} ) + log_{3}(0.09) + log_{4}(256) \\ log_{2}( {2}^{ \frac{1}{2} } ) + log_{3}( \frac{ {3}^{2} }{ {10}^{2} } ) + log_{ {2}^{2} }( {2}^{8} ) \\ \frac{1}{2} log_{2}(2) + 2( log_{3}(3) - log_{3}(10) ) + \frac{8}{2} log_{2}(2) \\ \frac{1}{2} + 2 - 2 log_{3}(10) + 4 \\ 6.5 - 2 log_{3}(10)$

aproximando o log de 10 na base 3 para 2:

$6.5 - 2 \times 2 =2.5$