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Question

# Find the set of solution in log12(x2−6x+12)≥−2

A

(,2]

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B

[2, 4]

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C

[4,)

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D

[2,)

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Solution

## The correct option is B [2, 4] log0.5(x2−6x+12)≥−2 --------(1) For log to be defined x2−6x+12>0 x2−6x+9+3>0 (x−3)2+3>0 We see that for any value of x. This is always true. Since, base of log in equation (1) lies between 0 to 1. So, given logarithm is a decreasing function. Then inequality is equivalent to So, x2−6x+12≤(12−2) x2−6x+12≤4 x2−6x+8≤0 (x−2)(x−4)≤0 So, x should be greater than 2 and less than 4 x ∈ [2,4]

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