Question

log6-x((x+5)/(x-6)^12)=>-12

Answer 1

$log__{6-x}}(frac{x+5}{x-6})^{12}ge-12\\12log__{6-x}}frac{x+5}{x-6}}ge-12\\log__{6-x}}frac{x+5}{x-6}}ge-1\\log__{6-x}}frac{x+5}{x-6}}ge log__{6-x}}(6-x)^{-1}\\frac{x+5}{x-6}gefrac{1}{6-x}\\frac{(x+5)(6-x)}{x-6}ge1\\-(x+5)ge1\\xle-6\\OD3:\left { {{frac{x+5}{x-6}}>0} atop {x<6, xne6}} right.quad => quad xin(-infty;-5)\\bf OTBET: xin(-infty;-6]$