how do you solve for the possible answers for log 16 base x+2 is equal to 2? What is the product of all possible solutions?
You must remember that logbx=y implies by = x.
so log(x+2)16 = 2 implies (x+2)2=16.
Next (x+2)2 = x2+4x+4
So x2+4x+4-16 = 0
Then x2+4x-12 = 0.
Using the quadratic formula (-b+√b2-4ac) / 2a gives us -6 and +2.
Therefore (-6)(2) = -12