are there people who are online still?then here is a question.Plz help me solve?

Question

Hey you mathemagicians! High I.Q Brains! Please Help me solve this problem?
Ok I am totally stuck with this problem.Plz help me solve it

If:
a^1/3 + b ^1/3 + c ^1/3 = 0 < "^" indicates power >
Prove that:
Log (a + b + c)/3 = 1/3 (log a + log b + log c)

Serious answers please
Dont answer just 4 the heck of geting 2 point!

Hey please help me i tried around a 1001 times!!!!!!!!!
thge question is correct

its log{(a+b+c)/3}

Answer 1

(a^1/3 + b^1/3 + c^1/3)=0
(a^1/3 + b^1/3 + c^1/3)^3=0
(a^1/3 +b^1/3)^3 +c + 3(a^1/3 + b^1/3)(c^1/3)(a^1/3 + b^1/3 + c^1/3)=0
a + b + 3(a^1/3)(b^1/3)(a^1/3 + b^1/3) + c = 0
a + b + 3(a^1/3 + b^1/3)(-c^1/3) + c= 0
(a+b+c)/3=(abc)^1/3
take log both sides: log{(a+b+c)/3}=1/3log(abc).
It's "legal" up to this step where all you need is for a+b+c and abc to be positive... The next step to get to final answer is not "legal" because not all a,b,c are positive numbers.

Answer 2

I don't think the question can be answered. In order for the if statement to be correct, at least a, b, or c is going to have to be less then or equal to 0 and logs are only defined for positive numbers.

Answer 3

a^1/3 + b ^1/3 + c ^1/3 = 0 is only true for a=b=c=0
It has nothing to do with
log{(a+b+c)/3} which is log(a+b+c) - log(3).
The last one follows from log(y/x) = log(y) - log(x)

Answer 4

LOGARITHMs ARE POSITIVE #S!!!!! MEANING THAT THE QUESTION IS UNDEFIND