Question

Descubra o valor de x e y:

${4}^{x} \times {8}^{y} = \frac{1}{4} \\ {9}^{x} \times {27}^{2y} = 3$
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Answer 1

Resposta:

$y = 1 \\ x = - 2.5$

Explicação:

${4}^{x} \times {8}^{y} = \frac{1}{4} \\ {2}^{2x} \times {2}^{3y} = {2}^{ - 2} \\ 2x + 3y = - 2 \\ x = \frac{ - 2 - 3y}{2} \\ \\ {9}^{x} \times {27}^{2y} = 3 \\ {3}^{2x} \times {3}^{6y} = {3}^{1} \\ 2x + 6y = 1 \\ 2 \times ( \frac{ - 2 - 3y}{2} ) + 6y = 1 \\ \frac{ - 4 - 6y}{ 2} + 6y = 1 \\ \frac{ - 4 - 6y + 12y = 2}{2} \\ 6y = 2 + 4 \\ y = \frac{6}{6} \\ y = 1 \\ \\ x = \frac{ - 2 - 3y}{2} \\ x = \frac{ - 2 - 3 \times 1}{2} \\ x = \frac{ - 5}{2} \\ x = - 2.5$