1. CH. 8.6 Natural Logarithms

2. Write 2 ln 12 – ln 9 as a single natural logarithm. 2 ln 12 – ln 9 = ln 12 2 – ln 9Power Property = lnQuotient Property 12 2 9 = ln 16Simplify. ALGEBRA 2 LESSON 8-6 Natural Logarithms 8-6

3. Check Understanding P. 462 # 1 A and C

4. Solve ln (2x – 4) 3 = 6. ln (2x – 4) 3 = 6 3 ln (2x – 4) = 6Power Property ln (2x – 4) = 2Divide each side by 3. 2x – 4 = e 2 Rewrite in exponential form. x = Solve for x. e 2 + 4 2 x 5.69Use a calculator. ALGEBRA 2 LESSON 8-6 Natural Logarithms 8-6

5. Check understanding P. 469 # 3 A and C

6. Use natural logarithms to solve 4e 3x + 1.2 = 14. 4e 3x + 1.2 = 14 4e 3x = 12.8Subtract 1.2 from each side. e 3x = 3.2Divide each side by 4. ln e 3x = ln 3.2Take the natural logarithm of each side. 3x = ln 3.2Simplify. x = Solve for x. ln 3.2 3 x 0.388 ALGEBRA 2 LESSON 8-6 Natural Logarithms 8-6

7. Check Understanding P. 464 #4A

8. Homework P. 464 # 2 – 28 even