Write the following as a single logarithms

Question

3log₂x+1/2log₂x-2log₂(x+1)

Answer 1

We will use the properties of logarithms to compact everything together.  Note that each term has a log₂.  This is great.

 

When we have a sum of logs, we can write as a product.  When we have a difference of logs, we can write as a quotient.  When the log has a coefficient, we can write this as an exponent.  We will do this process one step at a time.

 

 

log₂x³ + log₂x^1/2 - log₂(x +1)² =

 

log₂(x³ √(x) / (x + 1)²)