Question

como resolver ?2^log de 7 na base 2 + log de 3 na base 2

Answer 1

Propriedades que serão usadas:

$logb ^{n}=n*logb\\\\ log _{b}b=1$

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$2 ^{log _{2}7 }+log _{2}3=log _{2}7*2+log _{2}3\\ 2 ^{log _{2}7 }+log _{2}3=log _{2}7*log _{2}2+log _{2}3\\ 2 ^{log _{2}7 }+log _{2}3=\boxed{log _{2}}7*\boxed{log _{2} 2}+\boxed{log _{2}}3\\ 2 ^{log _{2}7 }+log _{2}3=7*1+3\\\\ \boxed{\boxed{2 ^{log _{2}7 }+log _{2}3=10}}$


Espero ter ajudado e tenha ótimos estudos =))