Question

Log de x na base 3 + 1 sobre Log de 9 na base 3x é igual a 2. Me ajudem!!!

Answer 1

$\mathrm{\log_3{x}+\dfrac{1}{\log_{3x}{9}}=2\ \to\ \log_3{x}+\log_9{3x}=2}\\\\ \mathrm{\log_3{x}+\log_{3^2}{3x}=2\ \to\ \log_3{x}+\dfrac{1}{2}\log_3{3x}=2}\\\\ \mathrm{\log_3{x}+\dfrac{1}{2}(\log_3{3}+\log_3{x})=2\ \to\ \log_3{x}+\dfrac{1}{2}(1+\log_3{x})=2}\\\\ \mathrm{\log_3{x}+\dfrac{1}{2}\log_3{x}+\dfrac{1}{2}=2\ \to\ \dfrac{3}{2}\log_3{x}=2-\dfrac{1}{2}}\\\\ \mathrm{\dfrac{3}{2}\log_3{x}=\dfrac{3}{2}\ \to\ \log_3{x}=1\ \to\ 3^1=x\ \to\ \boxed{\mathbf{x=3}}}$