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Question

# Identify which of the following statement(s) is(are) correct for the equation log(x2+2x−3)(4−log2(|x−1|+|x−3|))=0

A
The equation has exactly two solution
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B
The equation has more than two solutions
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C
The sum of all the solutions of the equation is 6
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D
The sum of all the solutions of the equation is 4
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Solution

## The correct option is C The sum of all the solutions of the equation is 6log(x2+2x−3)(4−log2(|x−1|+|x−3|))=0 log function is defined when (1) x2+2x−3>0⇒x∈(−∞,−3)∪(1,∞) (2) x2+2x−3≠1 ⇒x≠−1±√5 (3) log2(|x−1|+|x−3|)=3 ⇒|x−1|+|x−3|=8 ⇒x=−2,6 But x=−2 is not possible. ∴x=6

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