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If x, y, z are greater than 1 and form a geometric progression, then the numbers 1/(1 + log x), 1/(1 + log y), and 1/(1 + log z) belong to which progression?

1. A.P.
2. H.P.
3. G.P.
4. None of these

Correct answer: H.P.

Solution

Since x, y, z are in geometric progression, their logarithms log x, log y, and log z are in arithmetic progression. Consequently, the reciprocals of the sums of 1 and these logarithms will form a harmonic progression.

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