Complete the table

1. Complete the table What does a logarithm ask you for?

2. John Napier (1550-1617)Born1550Merchiston Tower, Edinburgh, ScotlandDied4 April1617Edinburgh, ScotlandResidenceScotlandNationalityScottishFieldMathematicianAlma materSt Andrews UniversityKnown forLogarithmsNapier's bonesDecimal notationInfluencesHenry BriggsReligious stanceProtestant Not a bad mathematical pedigree for a man who never finished university and who considered his most important work to be his Plaine Discovery of the Whole Revelation of St. John (1593)!

3. Napier lived during an age of great innovation in the world of astronomy. Copernicus had published his theory of the solar system in 1543, and many astronomers were eagerly involved in calculating and re-calculating planetary positions based in the wake of Copernicus's ideas. Their calculations took up pages and pages and hours and hours of work. Johannes Kepler (1571-1630) still had to fill nearly 1000 large pages with dense arithmetical computations to obtain his famous laws of planetary motions! Napier's logarithms helped ease that burden. Because they are exponents, logarithms allow tedious calculations (like multiplying and dividing very large numbers) to be replaced by the simpler process of adding and subtracting the corresponding logarithms. Not that mathematicians simply put down their pens after Napier. Many objected to using logarithms because no one knew understood they worked (an objection similar to one made to the use of computers in the 1960s)!

4. 8 .4 Exponential and Logarithmic Functions John Napier (1550-1617) Purpose Become familiar with a logarithm and Evaluate logarithmic functions with and without a calculator

5. LogarithmShow me the exponent!!!

8. Two equations with the same meaning Logarithmic form Exponential form logby= x bx=y

9. Two equations with the same meaning Logarithmic form Exponential form logby=x bx=y log232 =x

10. Change from logararithmic form to exponential form log232=x log51=x log1010=x log1/22=x

11. Evaluate the expression log381 log50.04 log1/28 log93

12. Common Logarithm log10x=logx If the base is 10 we don’t write it. It is just understood, because it is most commonly used

13. Natural logarithm logex=lnx If the base is e we don’t write it, we use the natural log button ln

14. Day 1 P. 490- 91 # 2-12 (even); 20-45 (by 5)

15. 8 .4 Exponential and Logarithmic Functions John Napier (1550-1617) Purpose Find the inverse of a function and Graph the logarithms

17. Simplify

18. Steps to find the inverse 1. Switch x and y 2. Write in exponential form 3. Solve for y

19. Steps to find the inverse 1. Switch x and y 2. Write in exponential form 3. Solve for y

20. Steps to find the inverse 1. Write in exponential form 2. Switch x and y 3. Solve for y

21. Steps to find the inverse 1. Switch x and y 2. Write in exponential form 3. Solve for y

22. Horizontal asymptote becomes Vertical Domain is restricted instead of Range b>1 up to the right 0<b<1 down to the right

24. Graph the function. State the domain and range

25. Graph the function. State the domain and range

26. Day 2 P. 490-92 # 1-13(odd); 16,22,28,34,49,54,56,64,82-90(even)