What is 3 ln 3 - ln 9 expressed as a single natural logarithm?

Solution:

Given: Expression is 3ln(3) - ln(9)

Let us apply the log formulas here.

Step1:

By using laws of logarithm

m × log(a) = log a^m

⇒ 3ln(3) = log(3³)

⇒ 3ln(3) = log(27)

Step2:

By using laws of logarithm

ln(a) - ln(b) = ln(a /b)

⇒ 3ln(3) - ln(9)

= ln(27/9) =ln(3)

⇒ 3ln(3) - ln(9) = ln(3)

What is 3 ln 3 - ln 9 expressed as a single natural logarithm?

Summary:

3 ln 3 - ln 9 can be expressed in a single natural logarithm as ln(3)