Question 991960
.
{{{log(4,(x-3))}}} - {{{log(16,(x-3))}}} = {{{1}}}.


Notice that {{{log(16,(x-3))}}} = {{{1/2}}}{{{log(4,(x-3))}}},     since     {{{16}}} = {{{4^2}}}.


So your equation takes the form


{{{log(4,(x-3))}}} - {{{1/2}}}{{{log(4,(x-3))}}} = {{{1}}},     or     {{{1/2}}}{{{log(4,(x-3))}}} = 1,     or     {{{log(4,(x-3))}}} = {{{2}}}.


The last equation means that 


{{{log(2,(x-3))}}} = {{{4}}},     since     {{{4}}} = {{{2^2}}}.


Hence,  x - 3 = {{{2^4}}} = 16  and then  x = 19.


<U>Answer</U>. &nbsp;x = 19.