Mack Exponecial

por ThaisP Ter 17 Dez 2013, 19:54

Se 2^x . 3 ^(x + 2) / 3 . 5^1-x = 1/50

entao x ² - 3 é igual a :
resposta: -2

por **ramonss** Ter 17 Dez 2013, 20:12

$Mack Exponecial Gif.latex?%5C%5C%5Cfrac%7B2%5Ex.3%5E%7Bx+2%7D%7D%7B3.5%5E%7B1-x%7D%7D%3D%5Cfrac%7B1%7D%7B2.5%5E2%7D%5Crightarrow%20%5Cfrac%7B2%5E%7Bx+1%7D.3%5E%7Bx+1%7D%7D%7B5%5E%7B-1-x%7D%7D%3D1%5C%5C%5C%5C%5C%5C2%5E%7Bx+1%7D.3%5E%7Bx+1%7D$

Enfim,

(-1)² - 3 = 1 - 3 = -2

por PedroCunha Ter 17 Dez 2013, 20:16

Veja:

$\frac{2^x \cdot 3^{x+2}}{3 \cdot 5^{1-x}} = \frac{1}{50} \therefore \frac{2^x \cdot 3^x \cdot 3^2}{3 \cdot \frac{5}{5^x}} = \frac{1}{50} \therefore \frac{9 \cdot 6^x}{\frac{15}{5^x}} = \frac{1}{50} \therefore \\\\ \frac{9 \cdot 6^x \cdot 5^x}{15} = \frac{1}{50} \therefore 30^x = \frac{15}{9 \cdot 50} \therefore 30^x = \frac{1}{30} \therefore 30^x = 30^{-1} \rightarrow x = -1 \\\\\circ x^2 - 3 = (-1)^2 - 3 = 1 -3 = -2$