Question

if a,b c are in GP PROVE THAT LOGA LOGB AND LOG C ARE
$in \: ap$

Answer 1

Let a,b c are in GP

Then , we know that

${b}^{2} = ac$

Taking log on both sides

$log( {b}^{2} ) = log(ac) \\ \\ using \: log \: property \\ \\ 2 log(b) = log(a) + log(c)$
It is the condition of AP

So loga, logb and logc are in AP

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