Confirm the equations

Question

log a/log b+c +log a/log c-b=2log a/log b+c ×log a/log c-b

Answer 1

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.