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Question
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
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Solution
a ,b and c are in G.P.
\[\therefore b^2 = ac\]
\[\text { Now, taking log on both the sides: } \]
\[ \Rightarrow \log \left( b \right)^2 = \log ac \]
\[ \Rightarrow 2\log b = \log a + \log c\]
\[\text { Thus, }\log a, \log b \text { and } \log\text { c are in A . P } .\]
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