Question

3^-log3^7 + 9^-log3^7 valendo 99 pontos

Answer 1

Esse é um caso bem especial, para resolver basta lembrar que:

$\Large\fbox{ \mathsf{a^{\ell og_aB}=B} }$

Portanto:

$\large\begin{array}{l}\mathsf{3^{-\ell og_37}~\Leftrightarrow~3^{\ell og_37^{-1}}~\Leftrightarrow~7^{-1}~\Leftrightarrow~\dfrac{1}{7}}\end{array}$


$\large\begin{array}{l}\mathsf{9^{-\ell og_37}~\Leftrightarrow~(3^2)^{\ell og_37^{-1}}~\Leftrightarrow~3^{2\ell og_37^{-1}}~\Leftrightarrow~3^{\ell og_37^{-2}}~\Leftrightarrow~7^{-2}}\\\\\mathsf{\dfrac{1}{7^2}~\Leftrightarrow~\dfrac{1}{49}}\end{array}$

Então:

$\large\begin{array}{l}\mathsf{3^{-\ell og_37}+9^{-\ell og_37}~\Longleftrightarrow~\dfrac{1}{7}+\dfrac{1}{49}~\Leftrightarrow~\dfrac{56}{343}~\Leftrightarrow~\dfrac{8}{49}}\end{array}$


Resposta letra B