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

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 log (a+b) /3 =1/2 * (      Log On


   

Question 478251: Respected Sir/Madam ,
Please help me to solve my logarithm problem . I Will be very grateful for your help. My question is :

if log (a+b) /3 =1/2 * (log a + log b) then what is the value of a/b + b/a ?
As the answer given is : 7
So please tell me steps for this problem ...
Thank you
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
1. a%2Fb%2Bb%2Fa=%28a%5E2%2Bb%5E2%29%2F%28ab%29
2. log+%28%28a%2Bb%29+%2F3%29+=%281%2F2%29+%2A+%28log+a+%2B+log+b%29 multiply both sides by 2
2log+%28%28a%2Bb%29+%2F3%29+=+%28log+a+%2B+log+b%29
Use loga%2Blogb=log%28%28ab%29%29, log%28a%2Fb%29=loga-logb,+n%2Aloga=log%28a%5En%29
log%28%28%28a%2Bb%29%2F3%29%5E2%29=log%28%28ab%29%29
log%28%28a%2Bb%29%5E2%2F9%29=log%28%28ab%29%29
log%28%28a%5E2%2B2ab%2Bb%5E2%29%29-log9-log%28%28ab%29%29=0
log%28%28a%5E2%2B2ab%2Bb%5E2%29%2Fab%29=log9
%28a%5E2%2Bb%5E2%29%2Fab%2B%282ab%29%2Fab=9
%28a%5E2%2Bb%5E2%29%2Fab%2B2=9
%28a%5E2%2Bb%5E2%29%2Fab=7