Question

Equaçao exponencial (1\3) ^-x+2 = raiz de 4 e 9

Answer 1

$\big( \frac{2}{3}\big) ^{-x+2} = \sqrt{ \frac{4}{9}}\\ \\\big( \frac{2}{3}\big) ^{-x+2} = \frac{2}{3}\\ \\\big( \frac{2}{3}\big) ^{-x+2} =\big(\frac{2}{3}\big)^1\\ \\-x+2=1\\ \\-x=1-2\\ \\-x=-1\\ \\x= \frac{-1}{-1} \\ \\x=1\\ \\S=\{1\}$

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$\big( \frac{1}{3}\big)^{-x+2}=\sqrt[4]{9}\\ \\\big(3^{-1}\big)^{-x+2}=\sqrt[4]{3^2}\\ \\\big(3^{-1}\big)^{-x+2}=3^\frac{2}{4}\\ \\3^{x-2}=3^\frac{2^{:2}}{4_{:2}}\\ \\3^{x-2}=3^\frac{1}{2}\\ \\x-2=\frac{1}{2}\\ \\x=\frac{1}{2}+2\\ \\x=\frac{1}{2}+\frac{4}{2}\\ \\x=\frac{1+4}{2}\\ \\x=\frac{5}{2}\\ \\ \\S=\big\{\frac{5}{2}\big\}$