Question

if x root of X equal to root of x power x then X equal to

Answer 1

the value of x=1

if x root of x is equal to xpower x then

$\sqrt[x]{x} = x \times x \\ \\ \sqrt[1]{1} = 1 \times 1$

Answer 2

The value of $x=\dfrac{3}{2}$.

Step-by-step explanation:

We have,

$x\sqrt{x} =x^{x}$

To find, the value of x = ?

∴ $x\sqrt{x} =x^{x}$

⇒ $x^{1} x^{\dfrac{1}{2}}=x^{x}$

⇒ $x^{\dfrac{3}{2}}=x^{x}$

[ ∵ $a^{m} .a^{n} =a^{m+n}$]

Equating the power of x, we get

⇒ x = $\dfrac{3}{2}$

Hence, the value of $x=\dfrac{3}{2}$.