How do you evaluate #log_169 (-13)#?
A log expression in this form is asking the question...
"what power of 169 will give -13?"
OR" What index of 169 will make -13?"
For any Real value of
So to find a value for
In general, if
Use the change of base formula to find:
#=(ln(13)+pi i)/(2 ln(13))#
#=1/2 + pi/(2ln(13))i#
This is the principal value of the Complex logarithm.
Other values that satisfy
I think that I could make a compromising answer.
Use that, for
If students are not to be burdened, these questions could be
reserved for Extraordinary Talent Examinations, after doing good
home work on the answer....