1 repeating digits 2,4,8,1,3,6,1,2,5,1 every 10th digit is a 1 tho this doesnt answer the q... EDIT: and is wrong as it all goes to pot relatively quickly... damnabbit
Sorry, a clever person already solved it for me If you are interested, you also get the value of log 3 (edited original question). I had exactly the same idea arran but it is incorrect
Write out log x for x from 1 to 10 (luckily you don't need 7 and you can do the rest easily) log 2^1000 = 1000 log 2 = 301.029996 so 2^1000 = 10^301 x 10^0.29996 and 0<0.029996<0.301 so 10^0 < 10^0.29996 < 10^0.301 so the first digit is a 1. basically, the decimal bit is the number that needs to be multiplied by the power of 1.
so 2^100000, then... log 2^100000 = 100,000 log 2 = 30102.9996 = 10^30102 x 10^0.9996
I think that question was in my Oxford admissions exam this year, but I think it was a smaller power and they also asked for the number of digits. Not that I could do that one, it always makes you feel better about yourself when a GCSE student can do Alevel maths better than you can...
I think that question was in my Oxford admissions exam this year, but I think it was a smaller power and they also asked for the number of digits. Not that I could do that one, it always makes you feel better about yourself when a GCSE student can do Alevel maths better than you can...
I've seen this question in the STEP booklet as well.
Yeah, I remember that question from the test. Funny thing is I got it right then but couldn't remember how to do it. I really do think I'm getting worse at Maths...
For the record it is Q1 on STEP I from 2000 (not in the booklet though?). The handwritten solutions that are floating around on the web do not show how to answer the question.
Interesting to hear a similar one was on the Oxford test...
Or perhaps Danniella should start to put a bit of effort into chemistry, physics and biology...
love danniella
lol, you'll be as good as me . No i kid its not that hard at all. I find maths a challenge 9 times out of 10 biology chemistry physics is just recalling facts.