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

 May 22, 2019
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2log ( a - 2b)  = log a + log b

 

log (a - 2b)^2  =  log (ab)        this implies that

 

(a - 2b)^2 = ab

                                                                          

a^2 - 4ab + 4b^2  = ab                                        

 

a^2 - 5ab + 4b^2  =  0       factor                      

                                                                      

(a - 4b) (a - b)  = 0

 

So  either

 

a - 4b = 0       or          a - b  =  0

a = 4b                          a  =  b

a/b  = 4                       a/b = 1

 

But the second solution means that we are taking the log of a negative number at some point

 

So

 

a/b = 4

 

 

cool cool  cool

 May 23, 2019

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