Subject: logs

Name: jessica
Who is asking: Student
Level: Secondary

Question:
Write as a single log 3ln x - 2ln(y+e) + 5ln(x-12) - 4ln y

There are three properties of the logarithm functions that allow you to make the simplification required. They are

1. log(ab) = log(a) + log(b)
2. log(a/b) = log(a) - log(b)
3. log(a^b) = a log(b)

I have written these in terms of log rather than ln since they are true for any logarithm. Looking at the first two terms of your problem, first apply property 3 and then property 2 to get

Now try the rest of the problem.