Question

25 elevado a (x) - 23×5 elevado a (x) = 50

Answer 1

$25^x-23*5^x=50\\ \\ (5^x)^2-23*5^x-50=0\\ \\ \boxed{y=5^x}\\ \\ y^2-23y-50=0\\ \\ S=\{ -2,25\}\\ \\ 5^x=25\\ \\ 5^x=5^2\\ \\ \boxed{x=2}$

Answer 2

$25^{x}-23\cdot5^{x}=50$

Observe que, $25^{x}=(5^2)^{x}=(5^x)^{2}$.

$(5^x)^{2}-23\cdot5^{x}-50=0$

$\Delta=23^2-4\cdot1\cdot(-50)=529+200=729$

$5^{x}=\dfrac{-(-23)\pm\sqrt{729}}{2}=\dfrac{23\pm27}{2}$

$5^{x}=\dfrac{23+27}{2}=25$

$5^{x}=\dfrac{23-27}{2}=-2$ (não serve)

$5^{x}=25~~\Rightarrow~~5^{x}=5^2~~\Rightarrow~~x=2$.