a²+b²=7ab show that log(a+b/2)=1/2loga+1/2logb
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Please write the problem less ambiguously: If
a2 + b2 = 7ab
Prove
log( (a+b)/3 ) = (1/2) (log a + log b)
The a+b/3 threw me off for a bit, so I almost didn't respond.
The first two things to consider is simplifying (log a + log b) and taking care of the (1/2) by multiplying both sides by 2.
Remember two important log rules
log xy = log x + log y
n log x = log xn
Notice that the given includes a2 + b2, as well as terms with ab, so it is also worth remembering that
a2 + 2ab + b2 = (a + b)2
The "creative problem solving" part is to add 2ab to both sides, then things should fall in to place.
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