Can there ever be any solution for log(-1)?

Question

My professor was giving us lecture about this logarithm chapter. He does mention that most important properties for log is - it's never equal to 1 and >o. And all of a sudden he goes like "try to find a solution for log(-1)".
Now I'm trying my best to get something. Can anybody out there help me? Even if you don't know the solution. Give me at least something that you know might be a possibility. Please friends, I need it.
Thanks,

thanks Michael M. for a good answer, and you are right I actually I meant about the domain. Thanks a log sorry lot. lol

Answer 1

the log of -1 is an imaginary number, just as the square root of -1 is imaginary.

If you are working in base 10, then to find the log of -1 you would have to answer the question " 10 to what power equals -1?" And of course, 10 to any power is positive, so there is no answer (on the real number line). I think that is all your professor was trying to get you to think about. Imaginary logs are for a more advanced course, after calculus.

But I think you have a few other things mixed up. the domain of the log function is x>0, but logs can be negative. And the log of whatever base you are using is equal to 1.

Answer 2

For the needs of your type, log(-a million) is undefined. whether, log(-a million) is a complicated huge style, yet this is oftentimes no longer stated till you're taking a complicated diagnosis course. the rationalization log(-a million) isn't a real huge style is here: assume there have been some authentic huge style x such that x = log(-a million) Then (i'm assuming base 10 logs right here) we've 10^x = -a million yet this is impossible because of the fact 10^x is often greater effective than 0 for any authentic huge style x. wish this permits.

Answer 3

how good is your imagination?