SOLUTION: If a^2 + b^2=5 ab.prove that 2 log (a+b)=log 7+log a+log b

Algebra.Com
Question 1043498: If a^2 + b^2=5 ab.prove that 2 log (a+b)=log 7+log a+log b
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
2 log (a+b)=log 7+log a+log b
log (a+b)^2=log (7ab)
raise to 10th power
(a+b)^2=7ab
a^2+2ab+b^2=7ab
but a^2+b^2=5ab
therefore, 5ab+2ab=7ab.
Answer by ikleyn(52851)   (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  = , then

 =     (after adding 2ab to both side)

 = .

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.


RELATED QUESTIONS

If a^2+b^2=7ab prove that 2 log(a-b)=log 5+log a+log... (answered by ikleyn)
log(a+b)/2 = ½(log a + log b) if a2+b2 = 7... (answered by Shin123)
If a^2+b^2=5ab,show that 2 log(a+b)=log 7 + log a + log... (answered by ikleyn)
if a^2+b^2=7ab,prove that log 1/3(a+b)=1/2[log a+log... (answered by CharlesG2)
If a^2 + b^2 =14ab, prove that log ((a+b)/4) = 1/2 (log a+log b... (answered by mananth)
If a^2+b^2=7ab,prove that log{1/3(a+b)}=1/2(log a + log b) (answered by ikleyn)
What is the value of the given expression: log AB^2 a. 2 log A log B b. 2 log... (answered by nerdybill)
If {{{ log ((a+b)/2) = (log a + log b) 1/2 }}} show that... (answered by robertb)
if Log ((a+b)/2) = 1/2 (log a + log b), show that a =... (answered by stanbon)