Find x if $$\log_x\left[\log_5(\sqrt{x + 5} + \sqrt{x})\right] = 0$$

$$\log_x\left[\log_5(\sqrt{x + 5} + \sqrt{x})\right] = 0$$

Shifting the 'x' from the base of LHS to the RHS, we get,

$$\log_5(\sqrt{x+5}+\sqrt{x})=x^0\ =\ 1$$

Now, shifting the '5' from the base of LHS to the RHS, we get,

$$\sqrt{\ x\ +\ 5}+\sqrt{x}\ =\ 5^1\ =\ 5$$

$$\sqrt{\ x\ +\ 5}\ =\ 5\ -\ \sqrt{\ x}$$

Squaring on both sides, we get,

$$\ x\ +\ 5\ =\ 25\ +\ x\ -\ 10\sqrt{\ x}$$

$$\ 10\sqrt{\ x}\ =\ 20$$

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

$$x\ =\ 4$$

Hence, the correct answer is option C.