Question

if x x√ x = ( x√ x) x find the value of x​

Answer 1

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Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $\left(x\sqrt{x}\right)^x = x^{x\sqrt{x}}$

To Find:

• Value of x

Solution:

$\implies \left(x\sqrt{x}\right)^x = x^{x\sqrt{x}} \\\\\implies \left(\sqrt{x^2*x}\right)^x = x^{x\sqrt{x}} \\\\\implies \left(\sqrt{x^3}\right)^x = x^{x\sqrt{x}}} \\\\\implies x^{\frac{3}{2}*x} = x^{x\sqrt{x}}} \\\\\text{As, bases are same, we compare the powers,} \\\\\implies \dfrac{3x}{2} = x\sqrt{x} \\\\\implies \dfrac{9x^2}{4} = x^2*x \:\:\:(On\: squaring\:both\:sides) \\\\\implies 9x^2 = 4x^3 \\\\\implies 9 = 4x \:\:\:\:\:(x^2\:gets \:cut)\\\\\bold{\implies x = \dfrac{9}{4}}$

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