this is the answer.... _+log_(_____)..... __ Meaning fill in the blanks

Question

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator. log₄(12x+8y)

Answer 1

When you have the log of a sum, there's not a lot you can do with it.  However, in this case you can factor 4 from the two terms:

 

log₄ (12x+8y)

= log₄ (4 (3x+2y))

 

Now use the product rule...

 

= log₄ 4 + log₄ (3x+2y)

 

Remember that the log of the base is always 1 (because the base raised to the first power is the base itself).  So that equals:

 

1 + log₄ (3x+2y)

 

That gives you the three things that go in the blanks