Question

Решите неравенства а) (√5)^(x-6)<1/5 б) (2/13)^(x^(2)-1)>=1

Answer 1

$( \sqrt{5} )^{x-6}< \frac{1}{5} \\5^{ \frac{1}{2}(x-6)}<5^{-1}\\ \frac{1}{2}(x-6)<-1\\x-6<-2\\x<-2+6\\x<4\\ \\( \frac{2}{13} )^{x^2-1} \geq 1 \\( \frac{2}{13} )^{x^2-1} \geq\frac{2}{13}^0\\ x^2-1 \leq 0\\(x-1)(x+1) \leq 0$

x∈[-1; 1]