Which system of equation can represent the equation?

         log(x+3)
y₁ =  --------------
            log(4)

         log(2 + x)
y₂ = ----------------
             log(2)

Explanation:

1) Here you must use the property named change of base of the logarithm.

That rule is:



2) Changing to base 10 that is:



3) Using it with the given equation, you get:



4) Now, to set your system you can make the left side of the equation equal to y₁ and the right side equal to y₂

         log(x+3)
y₁ =  -------------
           log(4)

         log(2 + x)
y₂ = ---------------
            log(2)

And that is your system which is the first choice of the list.