Question

find the value of x if(x√x)^x=x^x√x​

Answer 1

Answer:

please refer to the attachment

I hope it would help you

thank you.

Answer 2

$\underline{\red{ANSWER}}$

$\boxed{\rm{\pink{x=\frac{9}{4}}}}$

$\underline{\underline{\mathbb{EXPLANATION}}}$

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

$\implies{\rm{\left(x\times\:x^{\frac{1}{2}}\right)^x=x^{x\times\:x^{\frac{1}{2}}}}}$

$\implies{\rm{\left(x^{1+\frac{1}{2}}\right)^x=x^{x^{1+\frac{1}{2}}}}}$

$\implies{\rm{\left(x^{\frac{3}{2}}\right)^x=x^{x^{\frac{3}{2}}}}}$

$\underline{\boxed{\red{\rm{Now\:Compare\:Powers\:Of\:x\:We\:Have}}}}$

$\implies{\rm{\frac{3x}{2}=x^{\frac{3}{2}}}}$

$\implies{\rm{x\times\:x^{\frac{-3}{2}}=\frac{2}{3}}}$

$\implies{\rm{x^{1-\frac{3}{2}}=\frac{2}{3}}}$

$\implies{\rm{x^{\frac{-1}{2}}=\frac{2}{3}}}$

$\implies{\rm{\frac{3}{2}=x^{\frac{1}{2}}}}$

$\implies{\rm{\frac{3}{2}=\sqrt{x}}}$

$\underline{\underline{\red{\rm{SQUARING\:ON\: BOTH\:SIDES\:WE\:HAVE}}}}$

$\implies{\rm{x=\frac{9}{4}}}$

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