Question

Calcule o valor de log3 1/9 + log3 81.

Answer 1

$\large\begin{array}{l} \mathsf{\ell og_3\,\dfrac{1}{9}+\ell og_3\,81}\\\\ =\mathsf{\ell og_3\,\dfrac{1}{3^2}+\ell og_3\,(3^4)}\\\\ =\mathsf{\ell og_3\,(3^{-2})+\ell og_3\,(3^4)}\\\\ =\mathsf{-2\,\ell og_3\,3+4\,\ell og_3\,3}\\\\ =\mathsf{-2\cdot 1+4\cdot 1}\\\\ =\mathsf{-2+4}\\\\ =\mathsf{2}\qquad\checkmark \end{array}$


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$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


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Answer 2

$log_{3}( \frac{1}{9} ) + log_{3}(81) \\ {3}^{x} = \frac{1}{9} + {3}^{x} = 81 \\ {3}^{x} = {3}^{ - 2} + {3}^{x} = {3}^{4} \\ - 2 + 4 \\ 2$