Question

Решите пожалуйста данные примеры.

Answer 1

$5)9^{2\sqrt{x}}=3^{2x-6}\\\\3^{4\sqrt{x}}=3^{2x-6}\\\\4\sqrt{x} =2x-6\\\\(2\sqrt{x} )^{2} =(x-3)^{2}\\\\4x=x^{2}-6x+9\\\\x^{2}-10x+9=0\\\\x_{1}=1\\\\x_{2}=9$

$6)10^{x-\sqrt{x^{2}+5x+1}}=1000\\\\10^{x-\sqrt{x^{2}+5x+1}}=10^{3}\\\\x-\sqrt{x^{2}+5x+1 } =3\\\\(\sqrt{x^{2} +5x+1})^{2}=(x-3)^{2}\\\\x^{2}+5x+1=x^{2}-6x+9\\\\11x=8\\\\x=\frac{8}{11}$