1.

If a2 + b2 = 7ab, show thatlog(\(\frac{a+b}3\)) = 1/2 log a + 1/2 log b

Answer»

a2 + b2 = 7ab

a2 + 2ab + b2 = 7ab + 2ab

(a + b)2 = 9ab

\(\frac{(a+b)^2}9\) = ab

\((\frac{a+b}3)^2 = ab\) 

Taking log on both sides, we get

log\((\frac{a+b}3)^2=log (ab)\) 

2 log\((\frac{a+b}3)\)  = log a + log b

Dividing throughout by 2, we get

log\((\frac{a+b}3)=\frac12log\,a+\frac12 log\,b\)



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