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) \frac{1}{2}

Solve

x ln (x) = x ln (x) \frac{1}{2} : x = 1, x = 4

x = 1, x = 4

Verify Solutions:

x = 1

True

, x = 4

True

The solutions are

x = 1, x = 4

4^{2 x} - 4^{x} - 12 = 0

2^{x + 1} = 16

3^{x} e^{4 x - 1} = 5

9 = e^{2 x - 2}

2^{x + 5} \cdot 8 = 1 6^{2 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