Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calc

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. log₂(2x²+8x+8) 

Answer 1

Ok, first you're going to have to factor the function inside the log:

 

2x^2 +8x+8, you can use the quadratic formula and you'll get these factors:

 

(2x+4)(x+2)

 

Now you have log₂ ((2x+4)(x+2))

 

When you have multiplication inside logs that is equal to sdding logs 

 

log₂(2x+4) + log₂ (x+2)

 

Now from the first part you can factor out a 2 

 

2(x+2)

 

log (2) + log (x+2) + log (x+2)

 

And that's as far as it can expand