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Hi im stuck on this problem I need 

 

[2log2(x+5)=log2(x−9)+log2(x+53)+1.]

 Apr 4, 2020
 #1
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  2log2(x+5)  =    log2(x−9)   +  log2(x+53)+  1

 

Note  that   log 2 2   = 1

 

So  we  have

 

  2log2(x+5)  =    log2(x−9)   +  log2(x+53)+  log 2 2

 

And  by some log properties we  can simplify this as

 

log 2 ( x + 5)^2  =  log [ (x - 9) (x + 53) * 2 ]

 

The logs are the same so we can solve   this

 

(x + 5)^2  =  (x - 9) (x + 53) * 2

 

x^2 + 10x + 25 =  (x^2 + 44x -477) * 2

 

x^2 +10x + 25  = 2x^2  + 88x  - 954   rearrange as

 

x^2 + 78x   -979   =  0     factor as

 

(x + 89)  ( x - 11)   =0

 

Setting  each  factor  to 0  and solving for  x produces

 

x  = -89   reject....it makes the logs negativein the  original problem

 

x =  11   =  solution

 

 

 

cool cool cool

 Apr 4, 2020

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