First slide

Types of real valued functions XI

Question

If $\sqrt{\log_{2} x} - 0 .5 = \log_{2} \sqrt{x}$ then x equals

Moderate

A

odd integer
B

prime number
C

composite number
D

irrational

Solution

$\begin{array}{l} \sqrt{\log_{2} x} - 0 .5 = \log_{2} \sqrt{x} \\ or \sqrt{\log_{2} x} - 0 .5 = 0 .5 \log_{2} x \\ \Rightarrow y - 0 .5 = 0 .5 y^{2} \\ \Rightarrow y^{2} - 2 y + 1 = 0 \\ \Rightarrow y = 1 \\ \Rightarrow \log_{2} x = 1 \\ \Rightarrow x = 2 \end{array}$

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