Question

prove that log (xa÷xb)+log(xb÷xc)+log(xc÷xa)=0
​

Answer 1

Answer:

Formula used:-)

$log( \frac{m}{n} ) = log \: m - log \: n$

Using above formula

givan result can be proud very easily as::-)

LHS

$log( \frac{xa}{xb} ) + log(\frac{xb}{xc} ) + log( \frac{xc}{xa} ) \\ \\ = log( \frac{a}{b} ) + log( \frac{b}{c} ) + log( \frac{c}{a} ) \\ \\ = log \: a - log \: b + log \: b - log \: c + log \: c - log \: a \\ \\ = 0$

OR

Formula used:-)

$log \: m + log \: n = log(mn) \\ and \\ log1 = 0$

Using above formula it can also be proved as

$log( \frac{xa}{xb} ) + log(\frac{xb}{xc} ) + log( \frac{xc}{xa} ) \\ \\ = log( \frac{a}{b} ) + log( \frac{b}{c} ) + log( \frac{c}{a} ) \\ \\ =log( \frac{a}{b} \times \frac{b}{c} \times \frac{c}{a} ) \\ \\ = log1 \\ \\ = 0$

Answer 2

$log( \frac{xa}{xb} ) + log(\frac{xb}{xc} ) + log( \frac{xc}{xa} ) \\ \\ = log( \frac{a}{b} ) + log( \frac{b}{c} ) + log( \frac{c}{a} ) \\ \\ = log \: a - log \: b + log \: b - log \: c + log \: c - log \: a \\ \\ = 0$