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If {_{2}x}-0.5 = _{2}{x}, then the value of x is

Question

If $lo g_{2} x - 0.5 = lo g_{2} x$ , then the value of $x$ is

an odd integer.

a prime number.

a composite number.

an irrational number.

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Eleanor Discussed

lo g_{2} x - 0.5 = lo g_{2} x

, then the value of

x

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

lo g_{2} x = 0.5 + lo g_{2} x

, where

x > 0

For above equation to be defined,

lo g_{2} x > 0 \Rightarrow x > 1

\Rightarrow lo g_{2} x = \frac{1 + lo g _{2} x}{2} [∵ lo g a^{m} = m lo g a]

\Rightarrow (lo g_{2} x)^{2} - 2 lo g_{2} x + 1 = 0

\Rightarrow lo g_{2} x = 1

\Rightarrow x = 2

, which is a prime number.

Ans: B

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Question Text	If $lo g_{2} x - 0.5 = lo g_{2} x$ , then the value of $x$ is
Answer Type	Text solution:1
Upvotes	150