SOLUTION: Respected Sir/Madam , Please help me to solve my logarithm problem . I Will be very grateful for your help. My question is : If a^3 +b^3=0 then the value of log (a+b) -1/2 * (log

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Respected Sir/Madam , Please help me to solve my logarithm problem . I Will be very grateful for your help. My question is : If a^3 +b^3=0 then the value of log (a+b) -1/2 * (log      Log On


   

Question 478747: Respected Sir/Madam ,
Please help me to solve my logarithm problem . I Will be very grateful for your help. My question is :
If a^3 +b^3=0 then the value of log (a+b) -1/2 * (log a+ log b+ log 3)is equal to ?
As my Answer given is :0
So please mam provide me the steps for this logarithm question..
Thank you,
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
1. a%5E3%2Bb%5E3=%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29
if a%5E3%2Bb%5E3=0, then %28a%2Bb%29%28a%5E2-ab%2Bb%5E3%29=0, so
a%2Bb=0 or a%5E2-ab%2Bb%5E2=0
2. If we have log+%28%28a%2Bb%29%29+-%281%2F2%29+%2A+%28log+a%2B+log+b%2B+log+3%29 then a%2Bb can not be equal 0 (domain of the function log%28%28a%2Bb%29%29 is a%2Bb%3E0), so a%5E2-ab%2Bb%5E2 has to be equal 0

Use formula n%2Aloga=log%28a%5En%29, loga%2Blogb=log%28ab%29, loga-logb=log%28a%2Fb%29