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Question

The number of integral value(s) of a for which loge(x2+5x)=loge(x+a+3) has exactly one solution is

A
1
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B
4
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C
2
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D
5
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Solution

The correct option is D 5
loge(x2+5x)=loge(x+a+3)
For the log to be defined,
x2+5x>0x+a+3>0
Drawing the graph, we get


Now, loge(x2+5x)=loge(x+a+3) has 1 solution when x2+5x and x+a+3 intersect at exactly one point, which is possible when
5(a+3)<05a+3>02a>3a=2,1,0,1,2

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