One googol is the number 10^100 and one googolplex is a number 10^10^100. Let n be the largest whole number for which n^n < 10^10^100. how many digits does n have?

Answer 1

Hmmm. Take logs
log(n^n) < log(10^10^100)
n logn = 100 log(10^10)
n logn < 1000
n < 386.522