Question

Calcule o valor da expressão log2 8√2 - 2.log2 (log3 81)

Answer 1

Se a expressão for assim: $log_2{8 \sqrt{2} } - 2log_2{(log_3{81})}$
Então temos:

$log_2{8 \sqrt{2} } - 2log_2{(log_3{81})}\\\\ veja \ que: \ log_3{81}=4\\\\ log_2{8 \sqrt{2} } - 2log_2{4}\\\\ veja \ que: \ log_2{4}=2\\\\ log_2{8 \sqrt{2} } - 2.2\\\\ veja \ que: \ 8 \sqrt{2} =2^3.2^{\frac{1}{2}}=2^{3+{\frac{1}{2}}}=2^{\frac{7}{2}}\\\\ log_2{2^{\frac{7}{2}}} - 2.2\\\\ \frac{7}{2}log_22-4=\\\\ \frac{7}{2}-4=\frac{7-8}{2}\\\\ =\frac{-1}{2}$