Negative Numbers and Logarithms: Is it really wrong?

[Hepic]

I know that in logarithms we can not set as base a negative number,but look at this(in the brackets I will put the base.): log(-2)-8=3 Mathematics say that is wrong,but why?
If we tell -2^3=-8 we have a correct result.
So? Thank you!

 

[arildno]

That is certainly true.

But:
You'll only be able to find such matches for some INTEGER values.

With any positive number distinct from 1 as chosen as base, we can, with the associated logarithm function represent EVERY positive number as a power of our base.

Having a negative number as your base, however, you cannot gain this type of general usage, that is, a continuous logarithm function covering, say, all the negative numbers is impossible to construct.
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Thus, for simplicity, we say that you can't have a negative number as your base.

 

[Hepic]

That was very clear answer. I hope to be many other guys like you in this forum

 

[arildno]

You are welcome! There are many such guys here.