Log.x(1) = 0 and Log.x(x) = 1 so what is the value of Log.1(1) in the below summation? Is Log.1(1) defined or not? If not, why? Because Log.x(y)=z if and only if x^z=y and clearly 1^1 = 1 and also 1^0=1. Can anybody help please? I just came around this problem a day ago and couldn?t figure out why Log.1(1) should be undefined!

Posted on 2006-12-25 11:41:08 by XCHG

If i'm not mistaken, the sum on your picture is equal to 0, for real n, when n > 0 and n <> 1. Otherwise it is undefined, iirc. Long time no mathematical analysis ^^"
Posted on 2006-12-25 14:12:41 by ti_mo_n
Shouldnt it be 0? Since log base n 1 is always 0.
Posted on 2006-12-25 20:22:16 by roticv
XCHG,

Log.1(x) = 0

Log.1(x) = 0    means 1^0 = x , which is obviously wrong.

so what is the value of Log.1(1) in the below summation?

Log.1(1) = x    means 1^x = 1, in which case x can be zero or any positive number, so x is indefinite.

...clearly 1^1 = 0...

No, it is not very clear to me that 1^1  = 0 .  I would say that 1^1 = 1

...couldn?t figure out why Log.1(1) should be undefined

Because Log.1(1) is not a unique number.  It can be an infinite number of values.  Ratch

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
Posted on 2006-12-25 20:43:09 by Ratch
I must have been very sleepy when I posted this. I was going for Log.x(1) instead of Log.1(x) and Also 1^1 = 1 and 1^0=1.

So its Log.1(1) that was giving me a headache! Thank you guys. Appreciate it.
Posted on 2006-12-25 22:00:45 by XCHG