Re: HSC 2013 4U Marathon
If not using the calculator at all, the only logic I can think of is--> we know 2^10 (1024) is slightly greater than 10^3
So (2^10)^100 should be slightly greater than (10^3)^100=10^300--> So it should have slightly more than 300 digits, I would estimate 310(is that in give or take 50 range?)
Yep that is quite accurate of an estimate, the correct value is 302
Its better than my method though which was: (10^(log(2) * 1000) ), (using a calculator we get immediately that log(2) = 0.3016....) but my intention was for the answer to contain an attempt using integration to rationally approximate the value of log(2).
I was able to get like 340 using that lol
EDIT: It should be 302 since, 10^1 has 2 digits, 10^3 has 4 digits, thus 10^(301) should have 302 digits.