Question

if logp,logq,logn is in AP then p,q,r are will be?​

Answer 1

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Answer 2

$Given \: log \:p , log \:q \:and \: log \:r \: is \\an \: A.P$

$\blue { ( Difference \:of \: two \: consecutive }\\\blue { terms \: are \: equal \: in \: A.P )}$

$\implies log \: q - log \: p = log \: r - log \: q$

$\implies log \: \frac{q}{p} = log \: \frac{r}{q}$

$\boxed { \pink { Since , log \:m - log \: n = log \: \frac{m}{n} }}$

$\implies \frac{q}{p} = \frac{r}{q}$

$\implies q \times q = p \times r$

$\implies q^{2} = pr$

Therefore.,

$\green { p, q \: and \: r \: are \: in \:G.P . }$

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