Is it possible to solve this equation? Here is an equation that I found is quite impossible to solve without graphing or approximating the answer.
$$\sqrt{x} = 1+\ln(5+x)$$
I tried squaring both sides and factoring the $ln$ out, but it was no use. I also tried to get the procedure on WolframAlpha, but it doesn't have a procedure available for me.

As far as I know, there cannot be any solution to this equation because of the simultaneous presence of $\sqrt{x}$ and $x$. The only solution can be obtained using a numerical method such as Newton.  
$$x_{new} = x_{old} - \frac{f(x_{old})}{f'(x_{old})} $$
Starting at $x=1$, which we know is very far from the solution (see the graph of the function), the successive iterates are $6.357, 14.608, 16.536, 16.579$. Starting at $x=10$, the successive iterates are $15.968, 16.575, 16.579.$
If the equation were $x^k=1+\log(5+x^k)$, there is one or more analytical solutions in terms of Lambert function.
