If 6logx2 – 3logx3 = 3log50.2, find x.

If 6logx2 – 3logx3 = 3log50.2, find x.
  • A.
    8/3
  • B.
    4/3
  • C.
    3/4
  • D.
    3/8
Correct Answer: Option C
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

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