Question

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

Answer 1

Answer:

The value of x = $\frac{9}{4}$

Step-by-step explanation:

Given , $x^{x\sqrt{x} } = (x\sqrt{x} )^{x}$

Step 1:

we have

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

So, here we first solve the right hand side part which is

$(x\sqrt{x}) ^{x}$

Therefore , $x\sqrt{x} ^{x} = (x.x^{\frac{1}{2} } )^{x}$

⇒  $(x^{1+\frac{1}{2} }) ^{x}$= $(x^{\frac{3}{2} } )^{x}$  

⇒  $x^{\frac{3x}{2} }$.

Step 2:

Now , from the give question we have

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

Subtitute the value of $(x\sqrt{x}) ^{x}$ in the given equation

We have ,

$x^{x\sqrt{x} } = x^{\frac{3x}{2} }$

Here , we can see that the base of both the side is same ,

so compare the power of both side

⇒    $x\sqrt{x} = \frac{3x}{2}$

Cancle x from both side so we have ,

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

Now , squaring both the side  .

we get ,    $x = \frac{9}{4}$ .

Final answer :

Hence the required value of x = $\frac{9}{4}$ .