Question

Rezolvați in mulțimea numerelor reale ecuația 5^2x=125•5^-x

Answer 1

 

$\displaystyle\bf\\5^{2x}=125\cdot5^{-x}\\\\5^{2x}=\frac{125}{5^{x}}\\\\5^{2x}\cdot5^{x}=125\\\\5^{2x+x}=125\\\\5^{3x}=125\\\\5^{3x}=5^3\\\\3x=3\\\\x=\frac{3}{3}\\\\\boxed{\bf x=1}$