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  # help with algebra!! (logs)
  
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  Find a/b when 2log(a-2b) = log(a) + log(b).
  
  Mar 22, 2021
  
  #1
  +23
  +1
  
  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
  
  This implies that
  
  a = 4b   ⇒   a/b  =  4      or
  
  a - b  = 0  ⇒   a  = b  ⇒   a/b  =  1
  
  Mar 22, 2021
  #2
  +23
  0
  
  Hope this helps, feel free to tell me if i'm wrong :)
  
  Mar 22, 2021