Single Logarithm?

Question

Express as a single logarithm:

 

log (x+2) + log 1-3 log y

 

Not sure which rule to use here...really stuck.

Answer 1

Hey Mario.

 

Below are the rules we'll be invoking in order to approach this problem.

 

1. log(a/b) = log(a) - log(b)

 

2. log(a^b) = b*log(a)

 

3. log(1) = 0

 

**

 

Your function is below:

 

log(x+2) + log(1) - 3*log(y)

 

By rule number 3 above, we can eliminate the middle term. We're left with:

 

log(x+2) - 3*log(y)

 

By rule number 2 above, we can convert 3*log(y) to log(y^3). We're left with:

 

log(x+2) - log(y^3)

 

Finally, by rule number 1 above, we complete the question.

 

log[(x+2)/y^3)]

 

Hope this helps.