Question

Encontre o valor de x

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Quociente\,de\,bases\,iguais}\\\Huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{a^m}{a^n}=a^{m-n}}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\sf 3^{x-1}-3^{x-2}=54\\\sf \dfrac{3^x}{3}-\dfrac{3^x}{3^2}=54\\\\\sf \dfrac{3^x}{3}-\dfrac{3^x}{9}=54\\\rm multiplicando\,por\,9\,dos\,dois\,lados:\\\sf \dfrac{(9\div3)\cdot 3^x}{3\div3}-\dfrac{(9\div9)\cdot 3^x}{9\div9}=9\cdot 54\\\\\sf3\cdot 3^x-3^x=486\\\sf 2\cdot 3^x=486\\\sf 3^x=\dfrac{486}{2}\\\\\sf 3^x=243\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{r|r}\sf243&\sf3\\\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 243=3^5\\\sf 3^x=243\\\sf 3^x=3^5\\\sf x=5\\\sf \blue{S=\{5\}}\green{\checkmark}\end{array}}$