If log 1/4 (a + 2b) = 1/2 (loga + logb) then prove that a square + 4b square = 12ab
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a^2 + 4b^2 = 12ab
a^2 + (2b)^2+4ab = 12ab + 4ab
(a+2b)^2 = 16ab
Take log on both sides
2log(a+2b) = log16 + logab
log(a+2b) = 1/2 (4log2+logab)
log(a+2b)=2log2+1/2logab
a^2 + (2b)^2+4ab = 12ab + 4ab
(a+2b)^2 = 16ab
Take log on both sides
2log(a+2b) = log16 + logab
log(a+2b) = 1/2 (4log2+logab)
log(a+2b)=2log2+1/2logab
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