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Question

The sets of real values of x for which
log2x+3 x2<log2x+3 (2x+3)
includes


A

(32,1)

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B

(-1, 0)

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C

(0, 3)

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D

(,0)

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Solution

The correct options are
A

(32,1)


B

(-1, 0)


C

(0, 3)


The inequality (1) is equivalent to the following system of inequalities
0<2x+3<1X2>2x+3} (1)
or 2x+3>10<x2<2x+3} (2) Solving (1) first, we see that it is equivalent to3/2<x<1 and (x3)(x+1)>03/2<x<1 and (x<1 or x>3)3/2<x<1Next solving (2), we see that it is equivalent tox>1 and (x+1)(x3)<01<x<3Also, x0Hence, xϵ(3/2,1)(1,0)(0,3)


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