Question

Se $2 ^x = 4^y^+^1e27^y= 3^x^-^9$ determine o valor dese  determine o valor de y-x

resposta é : 5

Answer 1

$2^{x}=4^{y+1}\\2^{x}=(2^{2})^{y+1}\\2^{x}=2^{2*(y+1)}\\2^{x}=2^{2y+2}\\x=2y+2$
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$27^{y}=3^{x-9}\\(3^{3})^{y}=3^{x-9}\\3^{3y}=3^{x-9}\\3y=x-9$

Como x = 2y + 2:

$3y=2y+2-9\\3y=2y-7\\3y-2y=-7\\y=-7$

$x=2y+2\\x=2*(-7)+2\\x=-14+2\\x=-12$
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$y-x=-7-(-12)\\y-x=-7+12\\\\\boxed{\boxed{y-x=5}}$