Question

O resultado da equação exponencial (5/2)elevado a x=(25/4)elevado a x+2 é igual a:
a-4
b-2
c- -2
d- -4
E- 0

Answer 1

$\left(\dfrac{5}{2}\right)^{x}=\left(\dfrac{25}{4}\right)^{x+2}$

Veja que $\dfrac{25}{4}=\left(\dfrac{5}{2}\right)^2$

Logo

$\left(\dfrac{25}{4}\right)^{x+2}=\left(\left(\dfrac{5}{2}\right)^{2}\right)^{x+2}=\left(\dfrac{5}{2}\right)^{2x+4}$

Assim

$\left(\dfrac{5}{2}\right)^{x}=\left(\dfrac{5}{2}\right)^{2x+4}$

$x=2x+4 \iff 2x-x=-4 \iff \boxed{x=-4}$

$\texttt{Alternativa D}$