What is the answer to x^{sqrt(x)}=sqrt(x)^x ?

The answer to x^{sqrt(x)}=sqrt(x)^x is x=1,x=4

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

x^{x} = x^{x}

x = 1, x = 4

Solution steps

x^{x} = (x)^{x}

Apply exponent rules

x ln (x) = x ln (x)

Solve

x ln (x) = x ln (x) : x = 1, x = 4

x = 1, x = 4

Verify Solutions:

x = 1

True

, x = 4

True

The solutions are

x = 1, x = 4

12 5^{x} + 2 (2 5^{x}) - 3 (5^{x}) = 0

6^{x} = 2

6^{x} = 0

(3^{x - 1}) (5^{2 x + 1}) = 15

(\frac{1}{8})^{x} = 2

What is the answer to x^{sqrt(x)}=sqrt(x)^x ?
The answer to x^{sqrt(x)}=sqrt(x)^x is x=1,x=4
Solve for x: x^{sqrt(x)}=sqrt(x)^x
The solution is x=1,x=4