Find the largest integer n such that n^6021 < 2007^2007.?

3 ⤊

2007-12-07 16:53:52 · 3 answers · asked by Answer Seeker 1 in Science & Mathematics ➔ Mathematics

n^6021 = (n³)^2007 < 2007^2007
n³ < 2007
n < 2007^(1/3)
n < 12.6

n = 12

2007-12-07 17:00:48 · answer #1 · answered by Northstar 7 · 2⤊ 0⤋

Solve for n directly,
n < 2007^(2007/6021) = 12.61
Therefore, n = 12

2007-12-08 01:11:55 · answer #2 · answered by RobertJ 4 · 0⤊ 0⤋

(6021)ln(n)=2007ln2007

ln(n)=2.5347987883 .

Log(base e)(n)=2.5347987883

n = e^2.5347987883
n=12.61389246

Largest integer = 12 .

2007-12-08 01:03:40 · answer #3 · answered by Murtaza 6 · 1⤊ 0⤋