http://msdn.microsoft.com/en-us/library/system.string.lastindexofany.aspx
The LastIndexOfAny
method is what you're after. It will take an array of characters, and find the last occurrence of any of the characters.
var myString = "1/2-3+4*7";
var lastOperatorIndex = myString.LastIndexOfAny(new char[] { '+', '-', '/', '*' });
In this scenario, lastOperatorIndex == 7
If you're wanting to store the char itself to a variable you could have:
var myString = "1/2-3+4*7";
var operatorChar = myString[myString.LastIndexOfAny(new char[] { '+', '-', '/', '*' })];