1. 4.4 Evaluate Logarithms and Graph Logarithmic Functions Part 2

2. Definition Logarithms are the "opposite" of exponentials, Logs "undo" exponentials. Logs are the inverses of exponentials.

3. Writing Logarithms _____________________________________________ -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ____________________________________________ You read it: Log base “b” of “a” equals “c” ‘log’is the operation b is the base a is the object of the log c is what you get when you evaluate the log

4. Exponential Form log x y b = x y b = Logarithmic Form

5. Evaluating logarithms now you try some! Log 4 16 = Log 5 1 = Log 16 4 = Log 3 (-1) = (Think of the graph of y = 3 x ) 2 0 ½ (because 16 1/2 = 4) undefined

6. You should learn the following general forms!!! Log a 1 = 0 because a 0 = 1 Log a a = 1 because a 1 = a Log a a x = x because a x = a x

7. Common logarithms log x = log 10 x Understood base 10 if nothing is there.

8. Common Logs and Natural Logs with a calculator log 10 button ln e button

9. Finding Inverses Find the inverse of: y = log 3 x By definition of logarithm, the inverse is y=3 x OR write it in exponential form and switch the x & y! 3 y = x 3 x = y

10. Example 1: Write 5 3 = 125 in logarithmic form. Write log 3 81 = 4 in exponential form.

11. Try This: Complete the table. Exponential Form 2 5 = 323 -2 = 1/9 Logarithmic Form log 10 1000 = 3Log 16 4 = 1/2 #1#2#3#4

12. Lets look at their graphs y = x

13. To Evaluate Logs without a Calculator Change the log to an exponential. 1. log 2 32 = x 2. log 4 2 = x

14. Solve for x. 1. log 2 64 = x2. log x 343 = 3 Change the log to an exponential.

15. Evaluate without a calculator: 1.log 2 8 = x 2.log 2 1 = x 3. Find the value of k : k = log 9 3 4. Find the value of k : ½ = log k 9 5. Find the value of k : 3 = log 7 k Change the log to an exponential.

16. Common Logarithms Logarithms with base ______ are called common logarithms. Sometimes the base is assumed and not written. Thus, if you see a log written without a base, you assume the base is _______. The log button the calculator uses base _____. 10

17. Use your calculator to evaluate: 1. log 51 2. log 4 3. log 0.215 1.71 0.6 – 0.67 Which means

18. Do You Know What X is? 4. Solve for x: 10 x = 728 5. Solve for x: Change the exponential to a log. Then use calculator.

19. Remember e ?

20. Natural Logarithm A natural logarithm is a logarithm with base e, denoted by ln. A natural logarithm is the inverse of an exponential function with base e. Exponential Form Logarithmic Form

21. Lets look at their graphs y = x

22. Evaluate f(x)=ln x to the nearest thousandth for each value of x below: 0.693– 0.693 ? (see graph)

23. 13. Find the inverse of y = ln(x+1) 14. Find the inverse of y = 5 x. y = e x - 1 y = log 5 x

24. Homework Book Pg. 147 16 - 24 all Pg. 148 13 – 21 all