Question

Sabendo que 32 elevado a x+2 = 16 elevado a x+1 , como calcular o valor de x ao quadrado ?

Answer 1

$(a^{x})^{y} = a^{(x*y)}$
$a^{x} = a^{y} <=> x = y$
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$32^{(x+2)} = 16^{(x+1)}$
$(2^{5})^{(x+2)}=(2^{4})^{(x+1)}$
$2^{[5(x+2)]}=2^{[4(x+1)]}$
$2^{(5x+10)}=2^{(4x+4)}$
$5x+10=4x+4$
$5x-4x=4-10$
$x=-6$
$x^{2}=(-6)^{2}$
$x^{2}=36$

Answer 2

32^(x + 2) = 16^(x + 1)
(2)^5*(x + 2) = (2)^4*(x + 1)
5*(x + 2) = 4*(x + 1)
5x + 10 = 4x + 4
5x - 4x = 4 - 10
x = - 6

portanto: x^2 = ?
(-6)^2 = 36

resposta: 36