ln 20 – ln 18 + 2ln 6

Sure, let's solve this step by step using the properties of logarithms:

1. First, we can use the property of logarithms that states ln(a) - ln(b) = ln(a/b). So, ln 20 - ln 18 becomes ln(20/18) or ln(10/9).

2. Next, we can use the property of logarithms that states n*ln(a) = ln(a^n). So, 2ln 6 becomes ln(6^2) or ln(36).

3. Now, we can add these two results together. So, ln(10/9) + ln(36) becomes ln[(10/9)36] using the property of logarithms that states ln(a) + ln(b) = ln(ab).

4. Simplifying [(10/9)*36] gives us 40.

5. So, the final answer is ln(40).