Question 110929
{{{log((x+4))-log((x-3))=log ((8))}}}...........                apply  rule {{{log

((a/b)) = log((a))-log((b))}}}

{{{log(((x+4)/( x-3)))=log (8)}}}...    notice that bases are same, and      if 

{{{log b((x))= log b ((y))}}}, then {{{ x = y}}}; it means we can write:

{{{(x+4)/( x-3)= 8}}}...  multiply both sides by {{{x-3}}} 

{{{((x+4)/( x-3))(x-3)= 8(x-3)}}}...  cancel both {{{x-3}}} on the left 

side  and multiply by {{{8}}} on the right side   

{{{x+4= 8x – 24}}}......move {{{x}}} to the right and {{{-24}}} to the left

{{{4  + 24 = 8x – x}}}......

{{{28 = 7x }}}......divide both sides by {{{7}}}

{{{4 = x }}}......or

{{{x  = 4 }}}