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How do we solve this? ln(x-3)(x+1)=2ln3

 Nov 26, 2018
 #1
avatar+95866 
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 ln [ (x-3)(x+1) ]  = 2ln3       we can write

 

ln [ ( x - 3) ( x + 1) ] = ln 3^2      forget the natural logs

 

(x - 3) ( x + 1) =  3^2       simplify

 

x^2 - 2x - 3  = 9    subtract 9 from both sides

 

x^2 - 2x - 12 =  0         add 12 to both sides

 

x^2 - 2x    =  12        take (1/2) of 2 = 1....square this = 1...add to both sides

 

x^2 - 2x + 1  =    13      factor the left side

 

(x - 1)^2  =  13     take both roots

 

x - 1   = ±√13     add 1 to both sides

 

x = ±√13  + 1

 

 

cool cool cool

 Nov 26, 2018

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