2.  The logarithmic function log b (x) returns the number y such that b y = x.  For example, log 2 (8) = 3 because 2 3 = 8.  b is called the base of the logarithm.

3.  The natural logarithm is the logarithm with base e.  e is a mathematical constant that appears in many places. It’s an irrational number, but it can be approximated as 2.72.  This logarithmic function is often written ln(x).  ln(x) gives you the number y such that e y = x.

4.  The natural logarithm has all the same useful properties as any other logarithm:  ln(xy) = ln(x) + ln(y)  ln(x/y) = ln(x) – ln(y)  ln(x y ) = y * ln(x)

5. 1. What is ln(e 2 )? 2. What is ln(e)+ln(1)? 3. What is ln( )? 4. What is ln(68) – ln(25)? 5. What is ln(100)?

6. 1. ln(e 2 ) = 2ln(e) = 2 2. ln(1) = 0 and ln(e) = 1, so ln(e) + ln(1) = 1. 3. ln( ) = 1/2ln(e) = ½ 4. ln(68) – ln(25) = ln(68/25) = ln(2.72) ≈ 1 5. ln(100) ≈ 4.61. You’ll probably need a calculator for this one.