Question 1082504



{{{log(4,x) - log(16,(x+3)) = 1/2}}} 


{{{log(x)/log(4) - log((x+3))/log(16) = 1/2}}} 


{{{log(x)/log(2^2) - log((x+3))/log(2^4) = 1/2}}} 


{{{log(x)/2log(2) - log((x+3))/4log(2) = 1/2}}} .........both side multiply by {{{2}}}


{{{2log(x)/2log(2) - 2log((x+3))/4log(2) = 2(1/2)}}}


{{{log(x)/log(2) - log((x+3))/2log(2) = 1}}}  ....common denominator {{{2log(2)}}}


{{{(2log(x) - log((x+3)))/2log(2) = 1}}}


{{{2log(x) - log((x+3)) = 2log(2)}}}


{{{log(x^2) - log((x+3)) = log(2^2)}}}


{{{log(x^2/(x+3)) = log(4)}}}


{{{x^2/(x+3) = 4}}}


{{{x^2 = 4(x+3)}}}


{{{x^2 = 4x+12}}}


{{{x^2 -4x-12=0}}}


{{{x^2 +2x-6x-12=0}}}


{{{(x^2-6x) +(2x-12)=0}}}


{{{x(x-6) +2(x-6)=0}}}


{{{(x +2)(x-6)=0}}}


solutions:


{{{(x +2)=0}}}=>{{{x=-2}}}.....disregard negative solution


{{{(x-6)=0}}}=>{{{x=6}}}-> your solution