1ya theres something
i read all this log and its characteristics and all of that some time ago
sorry can't remember those things now [2]
ya but that post will help sir thanks [1]
34 Answers
1
1akand your approach was good
lets see this 210 =1024 or not ??
but yes now you can generalise and the theory should work till 64 i guesss
so the correct ans
till 10 -- 4 digits
till 20 --- 7 digits remember 20 -- 1 digit
.
.
.
60 - --- 19 digits
64 --- 20 digits
however this should be answer
though there has to be some other more "general" or "elegant" way of doing it
in general the no. two increases its digit count at powers ending with 4 , 7 ,0
there has to be a reason for it though which i don't know yet but i think this should be true
341log10 264 = 64 log10 2 = 64X 0.3010 (approx) = 19.264.
Characteristic = 19. Hence number of digits = 20
21HAD SEEN 2^60 AND 17^256 QUES IN TMH COZ I USE IT!!!!
WELL WELL PROPHET R U A MIND READER OR WAT????
I HAD JUS OPENED THE POST TO TYPE EXACTLY DA SOLN U POSTED......
HA HA....
1akand ur solution is also wrong...
see the trend
2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
i think answer should be 20
1ok since we've started on it now
forgive me but i can't control myself now
264 would have 65 digits when represented in binary won't it
log2264 = 64
hai na ??
yes i think i got it in fact 1 1 and rest 0s
341The idea is simply this. Log is a monotonically increasing function.
So if 10n≤x<10n+1
Then n ≤ log10 x < n+1
and so [log10 x] = characteristic of log10 x = n
So, if you know the characteristic, you know between what powers of 10 it lies. And that tells u how many digits becase if 10n≤x<10n+1, x has n+1 digits
1ya i got it
basically
log bx would tell the highest power of 'b' <= x
and that can tell us the no of digits in the no. if it is represnted in a no. system with base 'b' usually we take base 10 for normal work
and suddenly i start to wonder why [7]
okies lets leave that part
thanx again sir and yes sorry for replying late
62surbhi a small explanation (justification) of what prophet has done is this
Log 10 =1
log 100=2
log 1000=3
log 1000000=6
log 10n=n
11Philip, binomial expansion of 264 will have 65 terms in it and not 65 digits [1]
I also got confused at first [3]
1oh bro anirudh i was talking of the binary representation of 264 and not binomial expansion plz read carefully !!!
similarly the base 4 representation wud consist of log4264 +1 = 33 digits
plz don't concern yourself with this crap
1wel..........2power1 has 1
2power2 has 1
2power3 has 1
2power4 has 2
" 5 has 2
" 6 has 2
" 7 has 3 ..........in the same way for every 3 one digit increases........
so 2 power 64 has.........22 digits I GUESS.................
(THIS THEORY IS PURELY HYPOTHETICAL AND IT IS GIVEN BY ME )heheh
1example....... 1 +2+3+4+3+2+1............the middle number has 1 digit ..........but d sum is not single digit.