Could you Please solve this problem

[(86400*n^2)/2^n]<1 solve n

eawoodall

notice that
2^1 =2
2^2=4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10>1k
2^11 >2k
2^12>4k
2^13>8k
2^14>16k
2^15>32k
2^16>64k
2^17>128k
2^18>256k
2^19>512k
2^20>1M
2^21>2M
2^22=4,194304>4M


also notice
1^2=1
2^2=4
3^2=9
15^2=225
17^2=289
18^2=324
21^2=441
22^2=484

22^2 * 86400 = 484 * 86400 = 4,1817,600.

86400 * n^2 < 2^n when 86.k * n^2 < 2^n.

so at n=22 2^n > n^2 * 86400.

i hope that helps.

Rehaan_genius

in left hand side of the inequality, the denominator is always positive for all values of n so we can cross multiply, which gives:-
86400*n^2<2^n. so then find that value of n for which the inequality holds. i think you should first try yourself now!