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sas47
@sas47
June 2022
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nKrynka
Решение
log₂²x + 5log₂x + 6 > 0
log₂x = t
t² + 5t + 6 = 0
t₁ = - 2
t₂ = - 3
1) log₂x = - 2
x₁ = 1/4
log₂x = - 3
x₂ = 1/8
///////////////////---------------///////////-------->
-∞ 1/8 1/4 x
1) log₂x < 1/8
так как 2 > 1, то
x < 2¹/⁸
2) log₂x > 1/4
так как 2 > 1, то
x > 2¹/⁴
x ∈ (- ∞;
2¹/⁸
)∪(2¹/⁴; + ∞)
1 votes
Thanks 1
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Answers & Comments
log₂²x + 5log₂x + 6 > 0
log₂x = t
t² + 5t + 6 = 0
t₁ = - 2
t₂ = - 3
1) log₂x = - 2
x₁ = 1/4
log₂x = - 3
x₂ = 1/8
///////////////////---------------///////////-------->
-∞ 1/8 1/4 x
1) log₂x < 1/8
так как 2 > 1, то
x < 2¹/⁸
2) log₂x > 1/4
так как 2 > 1, то
x > 2¹/⁴
x ∈ (- ∞; 2¹/⁸)∪(2¹/⁴; + ∞)