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Find a/b when \(2\log{(a -2b)} = \log{a} + \log{b}\)

 Jun 28, 2022
 #1
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Note that a, b   are both positive

 

Using some log properties

 

log ( a - 2b)^2  =  log (a * b)

 

This means that

 

(a - 2b)^2  =  ab

 

a^2 - 5ab + 4b^2  = 0

 

(a - 4b) ( a - b)  = 0

 

Either                                          

 

a - b=   0        

 

a =  b

 

a / b  =  1      { this may produce a log of a  negative  - not  allowed }

 

Or

 

a - 4b  = 0

 

a = 4b

 

a / b =  4

 

The second is  correct

 

 

cool cool cool

 Jun 29, 2022
edited by CPhill  Jun 29, 2022

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