Question 933453
{{{log(2,(x+14))+log(2,x)=5}}}

{{{log(2,((x+14)*x))=5}}}

{{{log(2,(x^2+14x))=5}}}...in base {{{10}}}

{{{log((x^2+14x))/log((2))=5}}}

{{{log((x^2+14x))=5log((2))}}}

{{{log((x^2+14x))=log((2^5))}}}

{{{log((x^2+14x))=log((32))}}}...since log same, then

{{{x^2+14x=32}}}...solve for {{{x}}}

{{{x^2+14x-32=0}}}...write {{{14x}}} as {{{-2x+16x}}}

{{{x^2-2x+16x-32=0}}}...group

{{{(x^2-2x)+(16x-32)=0}}}

{{{x(x-2)+16(x-2)=0}}}

{{{(x-2)(x+16) = 0}}}

solutions:

if {{{(x-2) = 0}}} then {{{x=2}}}

if {{{(x+16) = 0}}} then {{{x=-16}}}...we cannot use this solution

so, your solution is: {{{highlight(x=2)}}}