Verified answer

lg(sqrt{8x+8} -1/2lg(x-13)=3lg2                      8x+8>0|:8

lg((8x+8)^(1/2))-1/2lg(x-13)=lg (2^3)             x-13>0

1/2lg(8x+8)-1/2lg(x-13)=lg8|*2

lg(8x+8)-lg(x-13)=2lg8                                   x>-1                          

lg(8x+8)/(x-13))=lg64                                    x>13

(8x+8)/(x-13)=64

8x+8=64x-832                                               x>13

56x=840

x=15>13

Ответ:15