Negatove roots are simply the reciprocals of the positive roots. So negative roots will exist if the number that you are taking a root of is not 0 and the positive root exists.
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Yes, the square root of negative 121 is undefined in the set of real numbers. However, in the set of complex numbers, the square root of negative 121 is equal to 11i, where i is the imaginary unit.
The answer does not exist because of complicated calculus. It is technically infinite or undefined because 0 - (negative) is the minor limit that is never reached.
Value of log 0 is negative infinity (undefined). Because no power can give an answer of zero. it is in fact undefined but written as negative infinity for symbolizing. Otherwise undefined and infinity are two different things.
Undefined: You cannot divide by zero
I am not quite sure what you mean with "log you"; the log is calculated for numbers. The following logarithms are undefined: For real numbers: the logarithm of zero and of negative numbers is undefined. For complex numbers: the logarithm of zero is undefined.