1. Sec 3.2 – Logarithmic Functions Definition of Logarithmic Function A logarithm is defined as follows:

2. Sec 3.2 – Logarithmic Functions

7. 2012 Pearson Education, Inc. All rights reservedSlide 3.2-7

8. Sec 3.2 – Logarithmic Functions Example: Solve for t.

9. Sec 3.2 – Logarithmic Functions The derivative of the natural logarithm of a function is derivative of the function divided by the function. Derivative of the Natural Logarithmic Function or Examples:

10. Sec 3.2 – Logarithmic Functions Examples:

11. Sec 3.2 – Logarithmic Functions Examples:

12. Sec 3.2 – Logarithmic Functions In a psychological experiment, students were shown a set of nonsense syllables, such as POK, RIZ, DEQ, and so on, and asked to recall them every second thereafter. The percentage R(x) who retained the syllables after t seconds was found to be given by the logarithmic learning model: Example: a) What percentage of students retained the syllables after 1 sec? b) Find R(2), and explain what it represents. a)

13. Sec 3.2 – Logarithmic Functions b) The result indicates that 2 seconds after students have been shown the syllables, the percentage of them who remember the syllables is decreasing at the rate of 13.5% per second. In a psychological experiment, students were shown a set of nonsense syllables, such as POK, RIZ, DEQ, and so on, and asked to recall them every second thereafter. The percentage R(x) who retained the syllables after t seconds was found to be given by the logarithmic learning model: a) What percentage of students retained the syllables after 1 sec? b) Find R(2), and explain what it represents.

14. 2012 Pearson Education, Inc. All rights reserved Sec 3.2 – Logarithmic Functions