Question

if x is equal to log 2 by 3 Y is equal to log 3 by 5 and Z is equal to log 5 by 2 then X + Y + Z is equal to zero prove it​

Answer 1

Step-by-step explanation:

Here ,

$x = log( \frac{2}{3} ) \\ y = log( \frac{3}{5} ) \\ z = log( \frac{5}{2} )$

● now ,

L.H.S. = X+Y+Z

$= log( \frac{2}{3} ) + log( \frac{3}{5} ) + log( \frac{5}{2} ) \\ = log( \frac{2}{3} \times \frac{3}{5} \times \frac{5}{2} )$

{ because loga+logb+logc = log (abc) }

$= log( \frac{30}{30} ) \\ = log(1) \\ = 0$

{ because log1 = 0 }

so ,

L.H.S. = R.H.S.