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Question

The values of x for which log3(x+2)(x+4)+log1/3(x+2)<12log37 holds, is

A
4<x<3
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B
x<3
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C
x>3
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D
2<x<3
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Solution

The correct option is D 2<x<3
Clearly, (x+2)(x+4)>0 and x+2>0
x>2 (1)

Now, log3(x+2)(x+4)+log1/3(x+2)<12log37
log3(x+2)(x+4)x+2<log37
log3(x+4)<log37
x+4<7
x<3 (2)

From (1) and (2),
2<x<3

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