If x-x1-5-8x-1 and x-0- then x - 2-2-2-4464

The correct option is D 64 x/x^1.5=8x^ 1 = x/x^1.5=8x^ 1 ⇒x/x^1.5= 8/x⇒x^2/x^1.5=8 ⇒ x^2 1.5 = 8 ⇒ x^0.5=8 ⇒ x^1/2=8 Squaring, ⇒ x = (8)^2=64 ∴ x = 64 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If x/x1.5=8x-...

Question

If $\frac{x}{x^{1.5}} = 8 x^{- 1} a n d x > 0, t h e n x =$

$\frac{\sqrt{2}}{4}$

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$2 \sqrt{2}$

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Solution

$\frac{x}{x^{1.5}} = 8 x^{- 1} \Rightarrow \frac{x}{x^{1.5}} = \frac{8}{x} \Rightarrow \frac{x^{2}}{x^{1.5}} = 8 \Rightarrow x^{2 - 1.5} = 8 \Rightarrow x^{0.5} = 8 \Rightarrow x^{\frac{1}{2}} = 8 S q u a r i n g, \Rightarrow x = (8)^{2} = 64 ∴ x$ = 64

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If xx1.5=8x−1andx>0,thenx=

xx1.5=8x−1⇒xx1.5=8x⇒x2x1.5=8⇒x2−1.5=8⇒x0.5=8⇒x12=8Squaring,⇒x=(8)2=64∴x = 64

If $\frac{x}{x^{1.5}} = 8 x^{- 1} a n d x > 0, t h e n x =$

$\frac{x}{x^{1.5}} = 8 x^{- 1} \Rightarrow \frac{x}{x^{1.5}} = \frac{8}{x} \Rightarrow \frac{x^{2}}{x^{1.5}} = 8 \Rightarrow x^{2 - 1.5} = 8 \Rightarrow x^{0.5} = 8 \Rightarrow x^{\frac{1}{2}} = 8 S q u a r i n g, \Rightarrow x = (8)^{2} = 64 ∴ x$ = 64