-log-2x-0-5-log-2-x- then x equals - 4-16-8-None of these-

The correct option is D None of these √(log_2x) 0.5=log_2√(x) (log_2x)^1/2=1/2+1/2log_2x log_2x=1/4+1/4(log_2x)^2+1/2log_2x (log_2x)^2 2log_2x+1=0 (log_2x ...

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Byju's Answer

Standard X

Mathematics

Fundamental laws of logarithms

√(log_2x)-0.5...

Question

$\sqrt{l o g_{2} x} - 0.5 = l o g_{2} \sqrt{x}$ , then x equals

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None of these

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Solution

The correct option is D
None of these

$\sqrt{l o g_{2} x} - 0.5 = l o g_{2} \sqrt{x} (l o g_{2} x)^{\frac{1}{2}} = \frac{1}{2} + \frac{1}{2} l o g_{2} x l o g_{2} x = \frac{1}{4} + \frac{1}{4} (l o g_{2} x)^{2} + \frac{1}{2} l o g_{2} x (l o g_{2} x)^{2} - 2 l o g_{2} x + 1 = 0 (l o g_{2} x - 1)^{2} = 0 l o g_{2} x = 1 x = 2$

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$\sqrt{l o g_{2} x} - 0.5 = l o g_{2} \sqrt{x}$ , then x equals

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√log2x−0.5=log2√x, then x equals

The correct option is D None of these √log2x−0.5=log2√x(log2x)12=12+12log2xlog2x=14+14(log2x)2+12log2x(log2x)2−2log2x+1=0(log2x−1)2=0log2x=1x=2

$\sqrt{l o g_{2} x} - 0.5 = l o g_{2} \sqrt{x}$ , then x equals