If a,b,c are in G.P., then $l o g_{a} n, l o g_{b} n, l o g_{c} n$ are in

A.P.

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G.P.

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H.P.

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None

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Solution

The correct option is C H.P.
$b^{2} = a c \Rightarrow 2 l o g b = l o g a + l o g c$
$∴ l o g_{n} a, l o g_{n} b, l o g_{n} c$ are in A.P.
Their reciprocals $l o g_{a} n, l o g_{b} n, l o g_{c} n$ are in H.P.

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Similar questions

a, b, c

l o g a

l o g b

l o g c

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

a > 0, c > 0, b = \sqrt{a c}, a, c

a c \neq 1, N > 0

\frac{1}{2} \frac{{log}_{a} N}{{log}_{c} N} = \frac{{log}_{a} N - {log}_{b} N}{{log}_{b} N - {log}_{c} N}

[l o g_{b} a l o g_{c} a - l o g_{a} a] + [l o g_{a} b l o g_{c} b - l o g_{b} b] + [l o g_{a} c l o g_{b} c - l o g_{c} c] = 0

If 3 numbers a,b,c are in G.P., then $l o g a, l o g b, l o g c$ are in:

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