Question

Resolva a equação exponencial
8^2-x= (0,25)^x+1

Answer 1

Boa tarde Leiidh!

Solução!

$8^{2-x}=0,25^{x+1} \\\\\\\ 8^{2-x}= \left ( \dfrac{25}{100} \right ) ^{x+1} \\\\\\\ Lembrando~~que~~0,25=\left ( \dfrac{25}{100} \right )= \dfrac{1}{4}\\\\\\\ 2^{3} ^{(2-x)}= \left ( \dfrac{1}{2^{2} } \right ) ^{(x+1)} \\\\\\\ 2^{3} ^{(2-x)}= 2^{-2} ^{(x+1)} \\\\\\\ Veja~~que~~as~~bases~~estao~~iguais!\\\\\\\ 2 ^{(6-3x)}= 2 ^{(-2x-2)} \\\\\\\ 6-3x=-2x-2\\\\\\\ -3x+2x=-2-6\\\\\\ -x=-8.(-1)\\\\\\ x=8\\\\\\\ \boxed{Resposta:x=8}$

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Bons estudos!