2004
Mathematics
JAMB
If 6logx2 - 3logx3 = 3log50.2, find x.
A.
8/3
B.
4/3
C.
3/4
D.
3/8
Correct Answer: 3/4
Explanation
6logx2 - 3logx3 = 3log50.2 = logx26 - 3logx33 = log5(0.2)3 = logx(64/27) = log5(1/5)3 logx(64/27) = log5(1/125) let logx(64/27) = y ∴xy = 64/27 and log5(1/125) = y ∴ 5y = 1/125 5y = 125-1 5y = 5-3 ∴ y = -3 substitute y = -3 in xy = 64/27 implies x-3 = 64/27 1/x3 = 64/27 64x3 = 27 x3 = 27/64 x3 = 3√27/64 x = 3/4
6logx2 - 3logx3 = 3log50.2 = logx26 - 3logx33 = log5(0.2)3 = logx(64/27) = log5(1/5)3 logx(64/27) = log5(1/125) let logx(64/27) = y ∴xy = 64/27 and log5(1/125) = y ∴ 5y = 1/125 5y = 125-1 5y = 5-3 ∴ y = -3 substitute y = -3 in xy = 64/27 implies x-3 = 64/27 1/x3 = 64/27 64x3 = 27 x3 = 27/64 x3 = 3√27/64 x = 3/4THIS WEEK's
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