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Question Number 132260 by Salman_Abir last updated on 12/Feb/21

Answered by Olaf last updated on 13/Feb/21

$${\left(x\sqrt{x}\right)}^x=x^{x\sqrt{x}}$$$${\left(x^{3/2}\right)}^x=x^{x^{3/2}}$$$$x\ln x^{3/2}=x^{3/2}\ln x$$$$x\ln x^{3/2}=x^{3/2}\ln x$$$$\frac{3}{2}x\ln x=x^{3/2}\ln x$$$$x\ln x[\frac{3}{2}-\sqrt{x}]=0$$$$(\mathrm{necessarilly}x\ne 0)$$$$x=1\mathrm{or}x=\frac{9}{4}$$

Commented by otchereabdullai@gmail.com last updated on 13/Feb/21

$$\mathrm{nice}\mathrm{one}\mathrm{sir}!$$

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