Question

2 elevado a 2+2 log2 5​

Answer 1

$2^{2\,+\,2log_{_2}5}~=\\\\\\Podemos~reescrever~o~expoente~da~seguinte~forma:\\\\\\=~2^{2\,.\,1\,+\,2log_{_2}5}\\\\\\=~2^{2\,.\,log_{_2}2\,+\,2log_{_2}5}\\\\\\Utilizando~a~propriedade~do~logaritmo~do~expoente,~temos:\\\\\\=~2^{log_{_2}2^2\,+\,log_{_2}5^2}\\\\\\=~2^{log_{_2}4\,+\,log_{_2}25}\\\\\\Utilizando~a~propriedade~do~logaritmo~do~produto,~temos:\\\\\\=~2^{log_{_2}(4\,.\,25)}\\\\\\=~2^{log_{_2}100}\\\\\\Utilizando~a~propriedade~~b^{log_{_b}a}~=~a}\,,~temos:$

$=~2\!\!\!\backslash^{log_{_2}\!\!\!\!\!\backslash100}\\\\\\=~\boxed{100}$