Lesson 3



DO NOT WRITE ON ME!

FOR USE ONLY AS A GUIDE TO TAKE NOTES IN YOUR NOTEBOOK!

Unit e Ln 2: Exponential vs. Logarithmic expressions

Definition of Logarithmic Function:

For x > 0, a > 0, and a ≠1, [pic] if and only if [pic].

[pic] because [pic]

The function [pic] is called the logarithmic function with base a.

(Read as “log base a of x”)

CONVERTING BETWEEN LOGS AND EXPONENTIAL EXPRESSIONS:

Convert the following functions into either exponential or logarithmic form:

|Exponential equation |Logarithmic equation |

| |log3243 |

|10-1 = 0.1 | |

| |log64(4) |

|45 = 1024 | |

| |log8512 |

|65 = 7776 | |

Evaluating Logs with the Definition of Logarithm:

Logarithm with base 10 such as [pic] is called common logarithm and is written as [pic]

(base 10 is “invisible”) Common Logarithm can be evaluated on the calculator. NOTE: LOG key on your calculator indicates common log with base 10 only!

Examples: Evaluate the following functions using the definition of logs.

1. [pic] 2. [pic] 3. [pic] 4. [pic]

Examples: Evaluate the following expressions, using the definition of logs:

5. log5(25). 6. log2(8). 7. log64(4).    8. log6(6). 9. log4(–16). 10. log2(0).

Important Logarithmic Identities are:

[pic] because [pic]

[pic] because [pic]

[pic] because [pic]

[pic] [pic] there is no way we can raise a positive base to some power

and end up with zero.

[pic] [pic] ( x = y

Evaluating Logs that do not simplify easily

There is a formula that you can use with logarithms that do not simplify easily. For instance, try to evaluate [pic].

Change of Base Formula: For any positive real numbers [pic]

This formula puts both logs into the base of 10, which your calculator can help you evaluate.

Examples: Evaluate the following expressions, using the change of base formula.

a. [pic] b. [pic] c. [pic]

Mixed Practice: Evaluate the following expressions/equations, using the definitions and properties of logs.

1. [pic] 2. [pic] 3. [pic] 4. [pic]

5. [pic] 6. [pic] 7. [pic] 8. [pic]

9. [pic] 10. [pic]=x 11. [pic] 12. [pic]

13. [pic] 14. [pic] 15. [pic] 16. [pic]

17. [pic] 18. [pic] 19. [pic] 20. [pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download