# Math notation question

In a book I am reading on modern physics (reading it yes, understanding it on the other hand… ) I’ve come across the following passage

My question is, what does the “exp” mean? does it mean the polynomial is raised to this power? Or does it mean the expression within the brackets is the base of an exponent? I haven’t ween this notation before.

later, in a discussion of half-life the book uses the following expression

``````x[sup]-n[/sup] =exp{-n lnx}

from high school algebra I know that
ln x[sup]-n[/sup] = -n lnx

But I'm having a bit of brain freeze on the exp{} notation.

Any help guys?  Thanks in advance``````

exp{x} is another notation for e[sup]x[/sup], where e is the base of the natural logarithm; “exp” is short for “exponential”. I’m not sure of the origin of this notation. It’s useful in computer programming but it’s also handy in mathematics, particularly when the exponent gets complicated. Now I’m curious which came first. Anyone?

exp(x) means e[sup]x[/sup].

x[sup]-n[/sup]
= (e[sup]lnx[/sup])[sup]-n[/sup]
= e[sup] - n ln x[/sup]
=exp{-n lnx}

Thanks!

I’ve just never seen this notation before.

For what it’s worth, exp(x) = sum(x[sup]n[/sup]/n!, 0 < n), and e is defined to be exp(1).

Silly people, exp is the map from a real Lie algebra to its simply-connected real Lie group. In this case, the algebra in question is the unique one-dimensional real Lie algebra.

The e[sup]x[/sup] came first. It turns out to be very useful in all sorts of old calculations (compound interest, etc…). For various reasons, e was considered the “most natural” base, and given one exponential function all others can be calculated. using logarithms in that base.

Anyhow, as more and more complicated expressions started showing up in the exponent, e[sup]x[/sup] was dubbed the exponential, and written as most functions are, so as not to unduly strain typesetters.