If $\log_{1/2}(x^2-5x+7)>0$ then exha

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $\log_{1/2}(x^2-5x+7)>0$ then exhaustive range of values of x is

Options:

(−∞, 2)∪(3, ∞)

(2, 3)

(−∞, 1)∪(2, ∞)

none of these

Correct Answer:

(2, 3)

Explanation:

$\log_{1/2}(x^2-5x+7)>0⇒x^2-5x+7≤(\frac{1}{2})0$

as $\frac{1}{2}<1$

So $x^2-5x+7<1⇒x^2-5x+6<0$

So $(x-2)(x-3)<0$

$⇒x∈(2, 3)$