Question

If x= log (a-b),y=log (a^2+ab+b^2), and z=log(a+b) find the relationship between x,y and z

Answer 1

Relationship between x,y,z is z = x + y

Step-by-step explanation:

Given :

• x = log ( a - b)
• y = log ( a² + ab + b² )

Look like z = log ( a³ - b³ )

=> z = log ( a³ - b³ )

Using identity a³ - b³ = ( a - b) ( a² + ab + b²)

=> z = log [ (a + b)( a² + ab + b² ) ]

Using Product rule log pq = log p + log q

=> z = log (a - b) + log( a² + ab + b² )

=> z = x + y

Hence the relation is z = x + y