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if x=0^0, thenlog0(x)=0log0(x)=ln(x)/ln(0)ln(x)=0x=1

log_{0}(x)=0 by definition.

Hi.Quote from: hamdani yusuf on 03/03/2022 22:18:44log_{0}(x)=0 by definition. You should ask yourself what or who's definition of a Logarithm you are using.Here's one example of a definition from Wikipedia: DefinitionThe logarithm of a positive real number x with respect to base b is the exponent by which b must be raised to yield x. So that definition only applies when both of the following things apply:i) x is a real number.ii) x > 0.In my opinion the Wikipedia definition isn't actually perfect either, for example it makes very little sense if the base b = 0 - but that's a separate issue.Best Wishes.

This isn't intended to be a criticism. What you've done is quite common and sensible.

Let's say that ln(0) is unknown. It can even be a complex number, for the sake of the argument.

What you have got is a proof that 00 =1 under certain assumptions:Assumption 1) That 0^{0} is a real number.Assumption 2) That 0^{0} > 0.

The answer was obtained as conclusion from the available definitions in mathematical operations.

What definition of a Logarithm are you using? Using your definition can you evaluate the following: 1. Log0(10) 2. Log10 (0)Most definitions for Logb(x) fail to give you a well defined function for some input numbers b and/or x.Best Wishes.

Reverse of exponential.

Log(10)/Log(0) = 1/(-~) =-0

How do you define "undefined" in mathematical sense?

Any number to the zeroth power is equal to 1 by definition.....(here's my website)....

That's a personal definition. I guess I did ask what definition you are using but I meant can you site a definition from a text-book or online reference.

An equivalent and more succinct definition is that the function log_{b} is the inverse function to the function .https://en.wikipedia.org/wiki/Logarithm#Definition

An equivalent and more succinct definition is that the function logb is the inverse function to the function .

So, you're saying that Log_{0} (10) = 0 if I've understood that correctly.So, by your definition of a Logarithm we have that 0^{ 0} = 10.How do you reconcile that with the proposal you made that 0^{0} = 1 ?

1. Take b= 0 as the base for the logarithm (or the exponentiation). 0^1 = 0 but also 0^2 = 0 and 0^ 3 = 1 etc.So which value do you map the value 0 back to when you try to invert that function? Is Log0 (0) = 1 , 2 or 3 ? To say that another way, exponentiation is sometimes a many-to-one function so that no inverse function exists. What I'm trying to say is that it isn't as simple as saying "Logarithms are just the reverse of exponentiation", sometimes you can't find a reverse procedure.

It might have been accidental but this editing has totally corrupted the original meaning. It's like quoting "Yes...I agree" from an extract that read "Yes that is interesting. However I can't agree with your conclusion".1. It's the last line in a block of text where the first lines were more specific and excluded certain values.2. There was a hyperlink on the word "inverse function" which has been lost. That link discusses the inability to find an inverse functions in some cases.

NOTE: I am not trying to be rude here. It just takes me hours to keep writing long posts. In the same style as your own posts, it's more useful to keep the points short and repeat anything that was important that was missed. If you want to have 00 =1 then that's fine by me. I was just assuming you wanted some discussion.

So, you're saying that Log0 (10) = 0 if I've understood that correctly.So, by your definition of a Logarithm we have that 0^0 = 10.How do you reconcile that with the proposal you made that 0^0 = 1 ?

as offered by Mascheroni.

What's 0 to the power of 0?