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Question

If log2x0.5=log2x, then x is

A
an odd integer
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B
a prime number
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C
a composite number
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D
an irrational number
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Solution

The correct option is B a prime number
Clearly, x>0, x>0
x>0 (1)
and log2x0
x1 (2)
So, from (1) and (2), x1

log2x0.5=log2x
log2x=0.5+0.5log2x
log2x=14(1+2log2x+(log2x)2)
4log2x=1+2log2x+(log2x)2
(log2x1)2=0
log2x=1
x=2

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