Match the reasons with the statements. given: x2 + 6x + 2x + 12 = 0 to prove: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 subtraction property of equality 2. x2 + 8x + 12 = 0 distributive postulate 3. (x + 6)(x + 2) = 0 combining like terms 4. x + 6 = 0 or x + 2 = 0 zero product postulate 5. x = -6 or x = -2

Given:

1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):

2. Distributive postulate:

The equation is

3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):

4. Subtraction property of equality:

a) subtract 6 from the first equation:

b) subtract 2 from the second equation:

1.x2 + 6x + 2x + 12 = 01. Given

2.x2 + 8x + 12 = 0        2. Combining like terms

3.(x + 6)(x + 2) = 0      3. Distributive Postulate

4.x + 6 = 0 or x + 2 = 04. Zero product postulate

5.x = -6 or x = -2         5 Subtraction property of equality

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)