1. Slide: 1 2.4 LOGARITHMS

2. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27 ? ? 2 = 16 Logarithm and its Relation to Exponents

3. Slide: 3 The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 How can we calculate this? log 81 9 9 = = log 27 3 3 = = log 100 7 7 = = Logarithm and its Relation to Exponents

4. Slide: 4 The logarithm of a number is the exponent by which a fixed number, the base, has to be raised to produce that number. Section 7.4 a x = y BaseExponent Number log y y a a x x = = Base Number Logarithm (Exponent) Exponential form Logarithmic form Logarithm and its Relation to Exponents

5. Slide: 5 The logarithm of a number is the exponent by which a fixed number, the base, has to be raised to produce that number. Section 7.4 4 3 = 64 5 4 = 625 Logarithm and its Relation to Exponents

6. Slide: 6 Most calculators can only solve for two special kinds of logarithms, the Common Logarithm (log) and the Natural Logarithm (ln). Section 7.4 10 2 = 100 Common Logarithms and Natural Logarithms

7. Slide: 7 Most calculators can only solve for two special kinds of logarithms, the Common Logarithm (log) and the Natural Logarithm (ln). Section 7.4 log 1 1 = 0 log 10 = 1 log 100 = 2 log 1000 = 3 Common Logarithms and Natural Logarithms

8. Slide: 8 Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number. Section 7.4 Natural logarithm button Common Logarithms and Natural Logarithms

9. Slide: 9 Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number. Section 7.4 e 2 = 7.39 log 7.39 e e = 2 ln 7.39 = 2 A logarithm to the base of e is called the natural logarithm. It is abbreviated as “ln”, without writing the base. Simply “ln” without a base implies log. e e = 2.718282 Common Logarithms and Natural Logarithms

10. Slide: 10 Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number. Section 7.4 ln 1 1 = 0 ln e e = 1 ln 10 = 2.302585… ln 1000 = 6.907755… Common Logarithms and Natural Logarithms

11. Slide: 11 Common logarithms (log) and natural logarithms (ln) follow the same rules. Section 7.4 Product Rule ln AB = ln A + ln B ln (2×3) = ln (15×25) = Rules of Logarithms

12. Slide: 12 Common logarithms (log) and natural logarithms (ln) follow the same rules. Section 7.4 Quotient Rule = ln A − ln B ln A A B B ( ( ) ) = = 3 3 2 2 ( ( ) ) = = 27 12 ( ( ) ) Rules of Logarithms

13. Slide: 13 Common logarithms (log) and natural logarithms (ln) follow the same rules. Section 7.4 Power Rule ln (A) n = nln A ln (10) 2 = ln (67) 4 = Rules of Logarithms

14. Slide: 14 Common logarithms (log) and natural logarithms (ln) follow the same rules. Section 7.4 0 as a power or 1 as logarithm ln (A) 0 = ln 1 = 0 ln (15) 0 = ln (32) 0 = Rules of Logarithms

15. Slide: 15 Solution 4 n = 65,536 Solve for “n” in the following equation.

16. Slide: 16 Solution Solve for “n” in the equation 36(2) n = 147,456.