meaning of "exp"

Probably means "exponent". But hard to say without seeing the original material. Could you post a photo of the page?

Here are two more examples:

How would the top equation be written without the exp functions?

Again, how to rewrite this expression without using the exp function? What is the meaning of "exp" in these equations?

Hi Allen. In this case I think exp(X) means "e" to the power X. Where "e" means Euler's number fully described here https://en.wikipedia.org/wiki/E_(mathematical_constant).

Hope this helps!

Also, in the equations above "ln" refers to the "natural logarithm" which is the logarithm to the base "e". 

Thinking a bit more about it! Also worth observing that exp(x) and ln(x) are the inverse functions of each other. So we can say:

exp(ln(x)) = ln(exp(x)) = x

David, you are right. Here is a great website that explains the whole thing:

https://wumbo.net/function/exponential/ 

Thanks for the held, Allen