SOLUTION: If a^2+b^2=5ab,show that 2 log(a+b)=log 7 + log a + log b?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If a^2+b^2=5ab,show that 2 log(a+b)=log 7 + log a + log b?      Log On


   

Question 1043492: If a^2+b^2=5ab,show that 2 log(a+b)=log 7 + log a + log b?
Answer by ikleyn(52863) About Me  (Show Source):
You can put this solution on YOUR website!
.
If a^2 + b^2=5 ab, then prove that 2 log (a+b)=log 7+log a+log b
~~~~~~~~~~~~~~~~~~~~ 

If a%5E2+%2B+b%5E2 = 5ab, then

a%5E2+%2B+2ab+%2B+b%5E2 = 5ab+%2B+2ab    (after adding 2ab to both side)

%28a+%2B+b%29%5E2 = 7ab.

Now take the logarithm of both sides (assuming a > 0, b > 0, which MUST be pointed in the condition, but mistakenly missed).
You will get

2*log(a+b) = log(7) + log(a) + log(b),   QED.

Solved.