What is the natural logarithm of -1?
there are no natural logarithms for negative numbers.
the only way it will work is if you use an imaginary number.
Example:
log√−1(−1) which is 2, since √−12=−1
With imaginary numbers there are other possibilities. Since ei*pi = -1 then ln(-1) = ln(ei*pi) = i*pi
More generally we could have ln(-1) = n*i*pi where n is any odd integer.