Help Please!!!

2log₂ ( x + 5)  =  log₂(x - 9) + log₂(x + 53)  +  1

Note  that  1  =  log₂ 2

So  we  have

2log₂ ( x + 5)  =  log₂(x - 9) + log₂(x + 53)  +   log₂ 2

By a couple of log properties we  can write

log₂ ( x + 5)^2  =  log₂  [ (x - 9)(x + 53)(2) ]

The log base is the same so we can solve  this

(x + 5)^2  = (x - 9) ( x + 53)(2)           simpify

x^2 + 10x + 25  =  (x^2  + 53x - 9x  - 477) (2)

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

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

x^2 +  78x  - 979   =  0        this can  be  factored as

(x  -11) ( x + 89)   =   0

Setting both factors to 0  and  solving for  x   gives  us

x  = 11    or  x   = -89

The second answer gives us the log of a negative  number in the original equation....so..... it's no good

The only answer is

x  = 11