# 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(3^{3})

⇒ 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)