2006-10-08 09:26:11 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x = 3^9999
log(x) = 9999 x * log(3) (base 10)
log(x) = 4770.735...
x = 10^4770.735...
Th
2006-10-08 09:36:14 · answer #1 · answered by Thermo 6 · 0⤊ 0⤋
To estimate it, start with 3^646 = 1.66085053 Ã 10^308.
Since 9999/646 = 15 309/646, 3^9999= (3^646)^15 * 3^309 = (1.66085053 Ã 10^308)^15 * 3^309 =
(1.66085053)^15 *10^(308*15) * 3^309 =
2018.1723 * 10^4620 * 2.69443498 Ã 10^147 =
2018.1723 * 2.69443498 * 10^(4620+147) =
5.43783404 * 10^(4620+147+3) =
5.43783404 * 10^4770 roughly.
Any more accurate takes pencil and paper and number theory (especially if you're just looking for the tens and units digits).
2006-10-08 16:43:03 · answer #2 · answered by maegical 4 · 0⤊ 0⤋
3^9999
=3^10000*3^(-1)
=5.44e+4770
(use x^y key on calculator.write 3, then press x^y,then press 9999.)
2006-10-08 16:38:05 · answer #3 · answered by Anonymous · 0⤊ 0⤋
log(3^9999)=9999*log(3)=4770.7354
3^9999=10^4770.7354=5.438*10^4770
2006-10-11 19:30:12 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
You could use differentials and increments, but that would be highly inaccurate. If you need accuracy, get out a calculator or a lot of scratch paper...
2006-10-08 16:32:34 · answer #5 · answered by mediaptera 4 · 0⤊ 1⤋
Ask a mathematician. It's
5.4378339511420862476775224306038*10^4770
See how easy that was? âº
Doug
2006-10-08 16:31:24 · answer #6 · answered by doug_donaghue 7 · 0⤊ 1⤋
just ring him
2006-10-08 16:43:30 · answer #7 · answered by neil d 3 · 0⤊ 1⤋