string length, exponent problems

I just started using Java, I completed my homework assignment in VB, but now I want to do it in java.
Problem: What is the largest value of n for which 2to the nth power has fewer than 100 decimal digits. Also, fewer than 1000 decimal digits?
I don't know how to tell the length of a string, or a double, or what ever type I should be using for this problem?
I also don't know how to raise a number to a power? I guess just using a loop and multplying it again and again? It seems there should be a better way, but I can't find it.
The more help the better, any code examples are greatly appriciated. I seem to learn best from them.

The java tutorial can be found here:
http://java.sun.com/docs/books/tutorial/
The java 1.4.2 API tells you about all the various classes and the information (class members) and services (methods) they offer.
To get the length of a String the String class (java.lang.String) seems a logical place to look. Check out the methods (see "method summary") of the String class and see what you find.
To get an exponent you should look at the Math (java.lang.Math) class methods.

Note that the Java API documentation can be found at http://java.sun.com/apis.html

As you're new to this Java programming, here is a list of free on-line Java tutorials and books that I have found useful that you might find useful as well.

Sun's Java Tutorial

Introduction to Computer Science using Java by Bradley Kjell

Introduction to Programming Using Java by David J. Eck

Dick Baldwin's Java Programming Tutorials

Interactive Programming In Java by Lynn Andrea Stein

Bruce Eckel's Thinking In Java

Then there is Head First Java It's purty cool for beginners.