Comparison of running times: Determine largest n to run in given time
That's the answer then. "It's so huge, it can't be written down at all". 

If an algorithm takes ln (n) microseconds, where n is the problem size, then there is no way to represent a problem that cannot be solved within a second. 

Your equation is absolutely fine, and the solution would be for example $n = e^{1,000,000}$. It's just a very, very large number. 

BTW. It's a very useful thing to look at. For example, if your computer can solve a problem of size n in an hour, you would want to know "what size of problem could I solve in an hour if I bought a computer that is twice as fast, or ten times faster".