If \(x^{x\sqrt{x}} = (x\sqrt{x})^x. then\, x\,is\,equal\,to\)(a) \(\f

1.	If \(x^{x\sqrt{x}} = (x\sqrt{x})^x. then\, x\,is\,equal\,to\)(a) \(\frac32\) (b) \(\frac29\) (c) \(\frac94\) (d) \(\frac49\)
Answer» (c) \(\frac94\) \(x^{x\sqrt{x}} = (x\sqrt{x})^x\) ⇒ \(x^{x\sqrt{x}} = (x^{\frac32})^x\) ⇒ \(x^{x\sqrt{x}} =x^{\frac{3}{2}x}\) ⇒ \(x\sqrt{x} = \frac32x ⇒\sqrt{x} =\frac32⇒x=\frac94.\)

If \(x^{x\sqrt{x}} = (x\sqrt{x})^x. then\, x\,is\,equal\,to\)(a) \(\frac32\) (b) \(\frac29\) (c) \(\frac94\) (d) \(\frac49\)

Answer»

(c) \(\frac94\)
\(x^{x\sqrt{x}} = (x\sqrt{x})^x\)

⇒ \(x^{x\sqrt{x}} = (x^{\frac32})^x\) ⇒ \(x^{x\sqrt{x}} =x^{\frac{3}{2}x}\)

⇒ \(x\sqrt{x} = \frac32x ⇒\sqrt{x} =\frac32⇒x=\frac94.\)