Date | May 2018 | Marks available | 6 | Reference code | 18M.1.hl.TZ1.5 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Solve | Question number | 5 | Adapted from | N/A |
Question
Solve (lnx)2−(ln2)(lnx)<2(ln2)2.
Markscheme
(lnx)2−(ln2)(lnx)−2(ln2)2(=0)
EITHER
lnx=ln2±√(ln2)2+8(ln2)22 M1
=ln2±3ln22 A1
OR
(lnx−2ln2)(lnx+2ln2)(=0) M1A1
THEN
lnx=2ln2 or −ln2 A1
⇒x=4 or x=12 (M1)A1
Note: (M1) is for an appropriate use of a log law in either case, dependent on the previous M1 being awarded, A1 for both correct answers.
solution is 12<x<4 A1
[6 marks]
Examiners report
[N/A]