What will be the dimension of $x$ in $e^x$?

Question

I just want to know if in an exponential function $e^x$, will $x$ always be dimensionless? If so, Why?

Does this answer your question? Exponential or logarithm of a dimensionful quantity?. See also, for instance, this one, or this one or this one, etc. — Yvan Velenik, Jun 19 '21 at 08:05
Why should this question be reopened? As I show in my comment above, there is already a multitude of similar questions on this site. It is insane to continue adding new ones all the time. — Yvan Velenik, Jun 19 '21 at 09:08

score 1 · Answer 1 · answered Jun 19 '21 at 08:09

1

Maclaurin series for the exponential function

$$e^{x} = \sum_{n=0}^{\infty} \frac{x^{n}}{n!}$$

So to be able to sum this up you have to have $x$ dimensionless.

answered Jun 19 '21 at 08:09

Monopole

So whenever we have any exponential function,the dimensions of the power will always be dimensionless? – Ritvish Jun 19 '21 at 08:11
Yes, otherwise the "answer" would be dependent on specific units chosen for $x$, to say the least. – Vladimir Kalitvianski Jun 19 '21 at 08:17

1 Answers1