Answer:
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.
