memory out of bounds

[sailingboarder]

when writing a program to solve the following problem, i ran out of memory.
i was programming in java, using longs
how can i properly solve this problem?

How many powers of 2 less than a googol begin with the digit 9?

[Lux Perpetua]

(In what follows, all logs are to base 10.) Hint: 2^k starts with 9 if and only if the fractional part of k*log(2) is more than log(9).