If k is an integer and 5^k<20,000, what is the greatest possible value of k?
Gee, please give me the whole idea of solving lorgarithem. of which I mean the whole process
2007-01-21 21:23:46 · 4 answers · asked by liangjizong22 1 in Science & Mathematics ➔ Mathematics
by the way, how do I take the log? I know nothing about log.
2007-01-22 00:07:44 · update #1
5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3,125
5^6 = 15,625
5^7 = 78,125
So the greatest k can be is 6.
2007-01-21 21:29:57 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
Take the log of each side of the inequality:
5^k < 20000
Log(5^k) < Log 20000
k*Log(5) < Log 20000
k < Log 20000 / Log 5 = 6.15
So k must be less than 6.15.
The important step here is to recognise that log(a^b) = b * log(a).
2007-01-22 06:18:16 · answer #2 · answered by Gnomon 6 · 0⤊ 0⤋
5^k<20.000 Taking log
k*log 5
2007-01-22 06:50:03 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
since 5^k < 20000
k < Log of (20000) at base 5
K< 6.153383
there fore K = 7
I hope it will help
2007-01-22 05:52:34 · answer #4 · answered by Laeeq 2 · 0⤊ 0⤋