Question

помогите пожалуйста с 6,7 надо решение​

Answer 1

$6.1)\sqrt{5^{-x} }=25^{\frac{5}{2} }\\\\5^{-\frac{x}{2} }=(5^{\frac{5}{2} })^{2}\\\\5^{-\frac{x}{2} }=5^{5}\\\\-\frac{x}{2} =5\\\\x=-10$

$6.2)(\frac{1}{\sqrt{5} })^{\sqrt{x} }=\frac{1}{25}\\\\(5^{-\frac{1}{2} })^{\sqrt{x} }=5^{-2} \\\\(5)^{-\frac{\sqrt{x} }{2} }=5^{-2}\\\\-\frac{\sqrt{x} }{2}=-2\\\\\sqrt{x}=4\\\\x=16$

Сумма корней равна :-  10 + 16 = 6

$7)(Sin\frac{5\pi }{6})^{6x+2}=64\\\\(Sin(\pi -\frac{\pi }{6}))^{6x+2}=2^{6}\\\\(Sin\frac{\pi }{6})^{6x+2}=2^{6}\\\\(\frac{1}{2})^{6x+2}=2^{6}\\\\2^{-6x-2} =2^{6}\\\\-6x-2=6\\\\6x=-8\\\\x=-\frac{4}{3}\\\\x=-1\frac{1}{3}$