Comparison of running times: Determine largest n to run in given time I am browsing the "Introduction to Algorithms" book by Thomas H. Cormen. One of the very first tasks in the introduction chapter gives a couple of running time functions like

f(n)=lg n
f(n)=n!
f(n)=2^n


and the following durations: 1second, 1minute, 1hour, 1 day, 1month, 1year, 1century

The f(n) functions describe the time taken in microseconds and for each duration I should determine the largest n which still runs in the given time.

Quite easy for potency and faculty, but I am stuck at the logarithm (lg n). Even for one second n gets so sooo huge and later even wolframalpha does not calculate it for 1 day. It is just too huge.

Or ist it wrong to try to calcualte these equations?

1.000.000 = lg n [for 1 second]
60.000.000 = lg n [for 1 minute]


...
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".