The system of equations can represent the equation is x^2+5x+7 = 0
The given logarithmic equation [tex]log_ab=x[/tex] expressed as indices is expressed as [tex]a^x=b[/tex]
Given the system of equation [tex]log_4(x+3)=log_2(2+x)[/tex]
This can be expressed as;
[tex]log_{2^2}(x+3)=log_2(2+x)\\2log_2(x+3)=log_2(2+x)\\log_2(x+3)^2=log_2(2+x)\\(x+3)^2=2+x[/tex]
Simplify the result to have:
[tex]x^2+6x+9=2+x\\x^2+6x-x+9-2=0\\x^2+5x+7=0[/tex]
Hence the system of equations can represent the equation is x^2+5x+7 = 0
Learn more on logarithm here: https://brainly.com/question/12049968
