Question

Log de 9 na base 1/2 ?

Answer 1

Olá.

Usaremos as seguintes propriedades:
$\diamondsuit~\Large\boxed{\boxed{\begin{array}{c}~\\\mathsf{log_{a^y}(b^x)=\dfrac{x}{y}\cdot log_a(b)}\\\\\mathsf{\dfrac{1}{n^1}=n^{-1}}\\~\end{array}}}$

Vamos a resolução:
$\Large\begin{array}{l}\mathsf{log_{\frac{1}{2}}(9)=}\\\\ \mathsf{log_{2^{-1}}(3^2)=}\\\\ \mathsf{log_{2^{-1}}(3^2)=\dfrac{2}{-1}\cdot log_2(3)}\\\\ \boxed{\mathsf{log_{2^{-1}}(3^2)=-2\cdot log_2(3)}}\end{array}$

Quaisquer dúvidas, deixe nos comentários.
Bons estudos$.$