Exponential of a large negative number

[Aadrych]

Hi,

I read on a previous post that to calculate the exponential of a large negative number I use the formula:
e^-r=10^(-rloge)
This is just a quick question but it it meant to be a log 10 or natural log and also is it meant to be loge⁰ or loge¹

Thanks in advance

 

[jbriggs444]

I read on a previous post that to calculate the exponential of a large negative number I use the formula:
e^-r=10^(-rloge)
This is just a quick question but it it meant to be a log 10 or natural log and also is it meant to be loge⁰ or loge¹

What is e raised to the zero power? What is the natural log of that? What is the base 10 log of that? Would either interpretation make any sense?

What is e raised to the first power? What is the natural log of that? Would that interpretation make any sense?

Can you use the law of exponents, (a^b)^c = a^bc to derive the formula in question?

 

[HallsofIvy]

It should be obvious that if that were a natural logarithm, then ln(e) would be 1 and there would be no reason to write it!
I can see no reason to as if the "e" is $e^0$ or $e^1$. Any number, a, by itself, is $a^1$. Any number, including e, to the 0 power is 1.