Question

Prove that : Log(26/33) - log (65/69) +log (55/46)=0

Answer 1

$log \: ( \frac{26}{33} ) - log \: ( \frac{65}{69} ) + log \:( \frac{55}{46} ) = 0 \\ LHS = log \: ( \frac{26}{33} ) - log \: ( \frac{65}{69} ) + log \:( \frac{55}{46} ) \\ = log \: ( \frac{26}{33} ) + log \:( \frac{55}{46} )- log \: ( \frac{65}{69} ) \: \\ = log \: ( \frac{26}{33} \times \frac{55}{46} )- log \: ( \frac{65}{69} ) \\ = log \: ( \frac{13}{3} \times \frac{5}{23} )- log \: ( \frac{65}{69} ) \\ = log \: ( \frac{65}{69} ) - log \: ( \frac{65}{69} ) \: \\ = 0 \\ = RHS \\ thus \: proved.$