log(a)/log(b+c)+log(a)/log(c-b)=(2log(a)/log(b+c))*(log(a)/log(c-b));
log(a)(1/log(b+c)+1/log(c-b))=2(log(a))^2/(log(b+c)log(c-b))
1/log(b+c)+1/log(c-b)=2log(a)/(log(b+c)log(c-b));
(log(c-b)+log(b+c)/(log(b+c)log(c-b)=2log(a)/(log(b+c)log(c-b));
log(c-b)+log(b+c)=2log(a);
log(c^2-b^2)=log(a^2);
c^2-b^2=a^2 or c^2=a^2+b^2 (Pythagoras' theorem, where a and b are the sides of a right-angled triangle and c is the hypotenuse).
CHECK:
If a=6, b=8, then c=10; log(6)/log(18)+log(6)/log(2)=(2log(6)/log(18))(log(6)/log(2));
3.2049=3.2049.