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What is log (100) ?

If you can, please post what degree you have and what field, for example:

Bachelor of Engineering: Civil

Thanks.

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- Thread starter caper_26
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- #1

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What is log (100) ?

If you can, please post what degree you have and what field, for example:

Bachelor of Engineering: Civil

Thanks.

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mathman

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Neither. Typically, out of habit, I use ##\log## to mean the base 10 logarithm. I've been meaning to break this habit ever since micromass told me that it was more agreeable with modern notation to use ##\log## for the natural logarithm. Now is as good a time as ever to do so, I guess.

What is log (100) ?

If you can, please post what degree you have and what field, for example:

Bachelor of Engineering: Civil

Thanks.

##\log(100)=\operatorname{Log}(100)+2\pi i n##, where ##\operatorname{Log}## is the principle value of the natural logarithm and ##n\in\mathbb{Z}##.

Your use of the word "is" along with the truncation of the decimal expansion of ##\operatorname{Log}(100)## disturbs me.

Remember that we define ##\log## as the inverse of exponentiation. Thus, if ##e^x=y##, then ##\log(y)=x##. Observe: $$e^t=e^t\cdot 1 \\ e^t=e^te^{2\pi i n}\quad (n\in\mathbb{Z}) \\ e^t=e^{t+2\pi i n} \\ \log(x)=t+2\pi i n \quad (\text{Here we have made the substitution } x=e^t).$$ We might even define, from this case, ##\operatorname{Log}(x)=t##. The point of this is that the natural logarithm is NOT a function from complex numbers to complex numbers. Instead, it is multivalued (unless we define it on something called a Riemann surface).

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