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Question
If `log x/(y - z) = logy/(z - x) = logz/(x - y)`, then prove that xyz = 1
Solution
Let `logx/(y - z)` = k
log x = k(y – z)
log x = ky – kz ......(1)
Similarly log y = k(z – x) = kz – kx ......(2)
log z = k(x – y) = kx – ky ......(3)
Adding (1), (2) and (3)
log x + log y + log z = ky – kz + kz – kx + kx – ky
log (xyz) = 0 = log 1
xyz = 1
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