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Find a/b when 2log(a-2b) = log(a) + log(b).

 Mar 22, 2021
 #1
avatar+69 
+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
avatar+69 
0

Hope this helps, feel free to tell me if i'm wrong :)

 Mar 22, 2021

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