1. NATURAL LOGARITHMS

2. The Constant: e e is a constant very similar to π. Π = 3.141592654… e = 2.718281828… Because it is a fixed number we can find e 2 e 3 - 1 2e 4

3. Converting between exponential & natural logs Use our rule from last week to convert y = e x to a logarithm.

4. Natural Logarithmic We call a log with a base of 10 “Common Log” We can call a log with a base of e “Natural Log” Natural Log is denoted with the “LN” If y = e x then ln y = x

5. Exponential to Log form 1.e x = 6 2. e x = 25 3. e x + 5 = 32

6. Log to Exponential Form 1.Ln 1 = 0 2.Ln 9 = 2.197 3.Ln (5.28) = 1.6639

7. Solving Exponential Equations 1.e x = 18 2.e x+1 = 30 3.e 2x = 12

8. Solving Logarithmic Equations 1.Ln x = -2 2.Ln (2m + 3) = 8 3.1.1 + Ln x 2 = 6

9. Natural Log (Ln) & e are inverses