Question

(raiz de 2)^log de raiz de 3 na base raiz de 2

Answer 1

$log_{b}(a)=c~~~\therefore~~~b^{c}=a$

Como c = log de a na base b:

$\boxed{\boxed{b^{log_{b}(a)}=a}}$
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$(\sqrt{2})^{log_{\sqrt{2}}(\sqrt{3})}$

Utilizando a propriedade mostrada acima:

$\boxed{\boxed{(\sqrt{2})^{log_{\sqrt{2}}(\sqrt{3})}=\sqrt{3}}}$