1. Logarithmic Functions

2. Example1. On the Richter Scale, the magnitude R of an earthquake of intensity I is given by where I 0 is a certain minimum intensity. R = log I I 0 If the intensity of an earthquake is 1000I 0 Find R.

3. Example1. The Richter Scale, R = log I I 0 If the intensity of an earthquake is 1000I 0 Find R. R = log 1000I 0 I 0 R = log 1000 R = 3

4. Example2. On the Richter Scale, the magnitude R of an earthquake of intensity I is given by where I 0 is a certain minimum intensity. R = log I I 0 Express I in terms of R and I 0

5. Example2. The Richter Scale, R = log I I 0 10 R = I/I 0 I = I 0 10 R

6. Example3. Newton law of cooling states that the rate at which an object cools is directly proportional to the difference in temperature between the object and it’s surroundings. The temperature T if an object at time t is given by T = 75 e -2t.

7. Example3. The temperature T if an object at time t is given by T = 75 e -2t. Express t as a function of T. T = 75 e -2t e -2t = T/75 -2t = ln T/75 t = - ln 1212 T 75