Question

log²5(25-x²)-3log5(25-x²)+2≥0

Answer 1

$log_5^2\left ( 25-x^2 \right )-3log_5\left ( 25-x^2 \right )+2\geq 0\\\left ( log_5\left ( 25-x^2 \right )-1 \right )\left ( log_5\left ( 25-x^2 \right )-2 \right )\geq 0\\log_5\left ( 25-x^2 \right )\in \left ( -\infty ;1 \right ]\cup \left [ 2;+\infty  \right )\\x\in \left ( -\infty ;-2\sqrt{5} \right ]\cup \left \{ 0 \right \}\cup \left [ 2\sqrt{5};+\infty  \right )\\25-x^2>0\Rightarrow x\in \left ( -5 ;-2\sqrt{5} \right ]\cup \left \{ 0 \right \}\cup \left [ 2\sqrt{5};+5  \right )$