If x=log3/5,y=log5/7,z=log root7/3,find the value of x+y+z

Given:

x=log(3/5)

y=log(5/7)

z=log(sqrt(7/3)

Find x+y+z

Steps:

Using the law of logarithms, log A + log B = log (AB), we get

x+y+z

=log(3/5)+log(5/7)+log(sqrt(7/3)

=log(3/5*5/7*sqrt(7/3))

=log(3/7*sqrt(7/3)

=log((sqrt(3/7)*sqrt(3/7)*sqrt(7/3))

=log((sqrt(3/7)*sqrt(3/7*7/3))

=log(sqrt(3/7)*1)

=log(sqrt(3/7))

Now apply another law of logarithms,  log(sqrt(A)) = (1/2) log(A)

=(1/2)log(3/7)

which is the final answer.

it would be 6xy and -16xy.