Mathematics

If a, b and c are in G.P., prove that :
log a, log b and log c are in A.P.

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Given, a, b and c are in G.P.

∴ b² = ac …….(i)

For, log a, log b and log c to be in A.P,

log b- log a = log c - log b

log b + log b = log a + log c

2log b = log a + log c

L.H.S. = 2log b = log b²

R.H.S. = log ac

Since, b² = ac,

L.H.S. = R.H.S.

∴ 2log b = log a + log c

Hence, proved that log a, log b and log c are in A.P.

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