Question

$25^{ \sqrt{x+2} } =125* 5^{ \sqrt{x+2} }$

Answer 1

[tex]\it 25^{\sqrt{x+2}} = 125\cdot 5^{\sqrt{x+2}} \Leftrightarrow (5^2)^{\sqrt{x+2}} = 5^3\cdot5^{\sqrt{x+2}} \Leftrightarrow \\\;\\ \Leftrightarrow 5^{2 \sqrt{x+2}} =5^{3 + \sqrt{x+2}} \Leftrightarrow 2 \sqrt{x+2} =3 + \sqrt{x+2} \Leftrightarrow \\\;\\ \Leftrightarrow 2\sqrt{x+2} - \sqrt{x+2} =3 \Leftrightarrow \sqrt{x+2} =3 \Leftrightarrow (\sqrt{x+2})^2 =3^2 \Leftrightarrow \\\;\\ \Leftrightarrow x +2= 9 \Leftrightarrow x = 7[/tex]