Find a/b when 2log(a-2b) = log(a) + log(b).
2 log (a - 2b ) = loga + log b
log (a - 2b)^2 = log (a*b)
This implies that
(a - 2b)^2 = ab
a^2 - 4ab + 4b^2 = ab
a^2 - 5ab + 4b^2 = 0
(a - 4b) (a - b) = 0
a = 4b ⇒ a/b = 4 or
a - b = 0 ⇒ a = b ⇒ a/b = 1
Hope this helps, feel free to tell me if i'm wrong :)
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