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

To solve the equation, we shall first shift the 'x' in the base to RHS, which makes $$x^0$$ or 1. 

Now, we will shift the '5' in the base to RHS, which becomes $$5^1$$ or 5 as the value in RHS. Meanwhile, the LHS becomes $$\sqrt{\ x+5}$$+$$\sqrt{\ x}$$.

Now, $$\sqrt{\ x+5}$$+$$\sqrt{\ x}$$ = 5.

The best way to proceed ahead is going through the options and substituting them in the equation. On doing so, we find out that x=4 would satisfy the equation and hence it is the correct answer.