Question

If x > 0 and $lo{g}_{2}x+lo{g}_2\left(\sqrt{x}\right)+lo{g}_2\left(\sqrt[4]{4x}\right)+lo{g}_2\left(\sqrt[8]{8x}\right)+lo{g}_2\left(\sqrt[16]{16x}\right)+.....=4$ then x equals-

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is C 4

We can write the given equation as
$lo{g}_2\left(x^{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....}\right)=4$

$\Rightarrow lo{g}_2\left(x^2\right)=4\Rightarrow x^2=2^4\Rightarrow x=4$