SATHEE: Quantitative Aptitude Ques 2046

Quantitative Aptitude Ques 2046

Question: If $ {x^{x\sqrt{x}}}={{(x\sqrt{x})}^{x}}, $ then x is equal to

Options:

A) $ \frac{4}{9} $

B) $ \frac{2}{3} $

C) $ \frac{9}{4} $

D) $ \frac{3}{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

$ {x^{x\sqrt{x}}}={{(x\sqrt{x})}^{x}} $
$ \Rightarrow $ $ {x^{x.{x^{1/2}}}}={{(x.{x^{1/2}})}^{x}} $

$ \Rightarrow $ $ {x^{x( 1+\frac{1}{2} )}}={{({x^{1+1/2}})}^{x}} $
$ \Rightarrow $ $ {x^{{x^{3/2}}}}={{({x^{3/2}})}^{x}}={x^{3x/2}} $

$ \Rightarrow $ $ {x^{{x^{3/2}}}}={x^{3x/2}} $ Base is same.

$ \therefore $ $ {x^{3/2}}=\frac{3x}{2} $

$ \Rightarrow $ $ {x^{3/2}}-\frac{3x}{2}=0 $
$ \Rightarrow $ $ x( {x^{\frac{1}{2}}}-\frac{3}{2} )=0 $
$ \Rightarrow $ $ x=0 $ or $ {x^{1/2}}=\frac{3}{2} $
$ \Rightarrow $ $ x={{( \frac{3}{2} )}^{2}}=\frac{9}{4} $ $ x=0 $ given indeterminate value.

$ \therefore $ $ x=\frac{9}{4} $

Quantitative Aptitude Ques 2045

Quantitative Aptitude Ques 2047

Quantitative Aptitude Ques 2046

Question: If $ {x^{x\sqrt{x}}}={{(x\sqrt{x})}^{x}}, $ then x is equal to

Options:

Answer:

Solution:

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