x^{x\sqrtx} = (x\sqrtx)^{6x} ⇒ x =

TS ICET 23 May 2019 Shift 1 Paper

Question : 77 of 200

Marks: +1, -0

x^{x√x}

(x√x)^{6x}

⇒ x =

Solution:

Given

x^{x √{x}}=(x √{x})^{6 x}

⇒ x^{x √{x}}=(x √{x})^{6 x}=x^{\;{3}/{2} × 6 x}=x^{9 x}

Comparing powers of equal bases, we get

x √{x}=9 x ⇒ √{x}=9

⇒ x=81

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