Question

resolver em R, a equação 3^2x-1 = 81

Answer 1

$\mathsf{3^{2x-1}=81~\Leftrightarrow~3^{2x}\cdot 3^{-1}=81~\Leftrightarrow~3^{2x}\cdot\dfrac{1}{3}=81~\Leftrightarrow~\dfrac{3^{2x}}{3}=81}\\\\\\\mathsf{3^{2x}=3\cdot 81~\Leftrightarrow~3^{2x}=243~\Leftrightarrow~\underbrace{~3^{2x}=3^5~}}\\\\\\\mathsf{Aplicando~log_3~em~ambos~os~lados~da~igualdade:}$

$\mathsf{\ell og_3(3)^{2x}=\ell og_3(3)^5~\Leftrightarrow~(2x)\ell og_3(3)=5\ell og_3(3)~\Leftrightarrow~(2x)\cdot 1=5\cdot 1}\\\\\\\mathsf{2x=5~\Rightarrow~}\fbox{ \mathsf{x=\dfrac{5}{2}} }$