Evaluate 5-\(^{3log_52}\) x 2\(^{2log_23}\)
A
8
B
11/8
C
2/5
D
1/8
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
5-3log52 x 22log23
i Let -3log52 = p => log52-3 = p
∴2-3 = 5p
∴5-3log52 = 5log52-3 = 5p
ii 22log23 = q => log532 = q
∴32 = 2q
∴222log23 = 2q
= 32 = 9
i x ii = 2-3 x 9 = 1/23 x 9
= 1/8 x 9
= 9/8 = 11/8
Source: Myschool Past Questions Archive (Record #10410)