What is the value of log1 to the base 1?

I want the value of logarithm of 1 to the base 1|||Any number will work.


1^1 = 1


1^0 = 1


1^120394871203492873 = 1|||It's undefined, as it was said above. To see this more clearly, assume log base 1 is defined. Then the algebra of logarithms holds for it, but if we attempt a base change to any base, let's say e, we have the following (calling log x the log of x to the base 1):





log1 = ln1/ln1 = 0/0





Do you see what I mean?|||There is NO log [base 1] logarithm !





log [base 1] (1) = any value





1 can not be changed exponentially !





QED|||Its indeterminate. Its the same problem as 0^0 or 0/0.





Its not technically undefined. Undefined implies no answer. Indeterminate implies infinite answers.|||log1/1


= 1* (log1)/1


= log 1|||It's 1. 1^1 = 1|||Log(1) 1 =x





1=1^x





x=0 ou x=1|||Let x = log₁(1), then by the definition of the logarithm, we need to find a number such that:





1^x = 1.





But recall that 1^x = 1 for ALL x. This means that log₁(1) can take ANY value. Hence, log₁(1) is not defined.





I hope this helps!