Question

VALENDO 30 PONTOS
Determine o valor de m e n da expressão 2^m+2.3^2n=288.

Answer 1

$\large\boxed{\begin{array}{l}\sf2^{m+2}\cdot3^{2n}=288\\\begin{array}{c|c}\sf288&\sf2\\\sf144&\sf2\\\sf72&\sf2\\\sf36&\sf2\\\sf18&\sf2\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 288=2^5\cdot3^2\\\sf 2^{m+2}\cdot3^{2n}=2^5\cdot3^2\\\sf m+2=5\\\sf m=5-2\\\sf m=3\\\sf 2n=2\\\sf n=\dfrac{2}{2}\\\\\sf n=1\end{array}}$