What a+b+c = if loga+log b+ log c=0

Question

What will be the value of sum of any numbers a+b+c if sum of logarithms of number i.e. log a +log b + log c =0

Answer 1

log a+log b+log c =0

log(abc)=0, abc=1, 1/c=ab.

(abc)^1/3≤(a+b+c)/3≤√(a²+b²+c²)/3

3≤a+b+c≤√3(a²+b²+1/(ab)²)≤3

So, a+b+c=3.

 

But you have to show that √3(a²+b²+1/(ab)²)≤3!