Log₂(5-x)logₓ₊₁1/8≥-6 ОДЗ 5-х>0 x<5 , x+1>0 x >-1; x+1≠1 x≠0
log₂(5-x)
----------------- ≥-6
log₁/₈ (х+1)
log₂(5-x)
----------------- ≥-6
log₂⁻³ (х+1)
log₂(5-x)
-------------------------- ≥-6
(-1/3) log₂(х+1)
log₂(5-x) ≥ -6* (-1/3) log₂(х+1)
log₂(5-x) ≥ 2 log₂(х+1)
log₂(5-x) ≥ 2 log₂(х+1)
log₂(5-x) ≥ log₂(х+1) ²
(5-x) ≥ (х+1) ²
5-x ≥ х²+2х+1
х²+3х-4 ≤ 0
D=9+16=25
x₁=(-3+5):2=1
х₂= (-3-5):2=-4
__+_____-4_____-_____1______+______
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с учетом ОДЗ х∈[-1;0)∪(0;1)