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If \(\frac{x}{{x^{1.5}}}\) = 8x-1 and x > 0, then x =

A.\(\cfrac{\sqrt{2}}{4}\)

B. \(2\sqrt{2}\)

C. 4

D. 64

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Best answer

\(\cfrac{x}{{x^{1.5}}}\) \(= 8x^{-1}\)

⇒ \(\cfrac{x}{{x^{1.5}}}\)\(= \frac{8}x\)

⇒ \(x^{1+1-1.5}\) = 8

⇒ \(x^\cfrac{1}{2}\) = \(64^\cfrac{1}{2}\)

⇒ x = 64

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