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Question

If log2x0.5=log2x, then x equals to

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
log2x0.5=log2x
For the equation to be defined,
log2x0 and x>0
x1 and x>0
x1

Now, log2x0.5=log2x
log2x12=12log2x
Let log2x=tt0
Then t12=12t
2t1=t(t)22t+1=0t=1t=1x=2

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