Question 1010177


{{{log(2 ,(256))= x+y}}} 
{{{log(3 ,(81))= x-y}}}

{{{log(2 ,(256))= x+y}}}........{{{256=2^8}}}

{{{log(2 ,(2^8))= x+y}}}

{{{8log(2 ,(2))= x+y}}}....since {{{log(2 ,(2))=1}}}, we have

{{{8*1= x+y}}}

{{{8= x+y}}}........eq.1


{{{log(3 ,(81))= x-y}}}

{{{log(3 ,(3^4))= x-y}}}

{{{4log(3 ,(3))= x-y}}}

{{{4*1= x-y}}}

{{{4= x-y}}}.................eq.2


solve the system:

{{{8= x+y}}}........eq.1
{{{4= x-y}}}.................eq.2
--------------------------------------add both eq.1 and eq.2

{{{8+4= x+y+x-y}}}

{{{12= x+cross(y)+x-cross(y)}}}

{{{12= 2x}}}

{{{x=12/2}}}

{{{highlight(x=6)}}}

go to {{{8= x+y}}}........eq.1, substitute {{{6}}} for {{{x}}} and solve for {{{y}}}

{{{8= 6+y}}}

{{{8-6=y}}}

{{{highlight(y=2)}}}