Question

log(p/q)+log(q/r)+log(r/p)=​

Answer 1

$log( \frac{p}{q} ) + log( \frac{q}{r} ) + log( \frac{r}{p} )$

$= log( \frac{p}{q} \times \frac{q}{r} \times \frac{r}{p} )$

$= log(1)$

$= log_{10}(1)$

$0$

Hence, the answer is 0.

Answer 2

$Given \: log \Big(\frac{p}{q}\Big) + log \Big(\frac{q}{r}\Big) + log \Big(\frac{r}{p}\Big)$

/* By Logarithmic law */

$\boxed{ \pink{ log m + log n = log ( m \times n ) }}$

$= log \Big( \frac{ p}{q} \times \frac{ q}{r} \times \frac{ r}{p} \Big)$

$= log \Big( \frac{pqr}{pqr}\Big)$

$= log 1$

$= 0$

$\boxed {\blue {\because log_{a} 1 = 0 }}$

Therefore.,

$\red{ log \Big(\frac{p}{q}\Big) + log \Big(\frac{q}{r}\Big) + log \Big(\frac{r}{p}\Big) } \green { = 0 }$

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