Question

If x√x=(x√x) ^x , then the value of x is

Answer 1

Answer:

Correct option is

D) 9/4

Step-by-step explanation:

x  

x  

x

​

 

=(x  

x

​

)  

x

 

=x  

x

⋅x  

(  

2

​

 

1

​

)⋅x

 

x  

x⋅x(  

2

1

​

)

=x  

x

⋅x  

2

x

​

 

 

x  

x(  

2

3

​

)

=x  

(  

2

3

​

)x

 

x  

2

3

​

 

=  

2

3

​

x

∴x  

x

​

=  

2

3

​

x⟹  

x

​

=  

2

3

​

⟹x=  

4

9

​

Answer 2

Answer:

x=1

Step-by-step explanation:

$x \times \sqrt{x} =( x \times \sqrt{x} )^{2} \\ = 1 = \frac{ {(x \sqrt{x)} }^{2} }{x \sqrt{x} } = (1 = x \sqrt{x}) \\ \\ 1 = {x}^{ \frac{3}{2} } = x = \sqrt[ \frac{2}{3} ]{1} = x = 1$