Lesson 5 6 Logarithms and Logarithmic Functions Advanced

Lesson 5 -6: Logarithms and Logarithmic Functions Advanced Math Topics

Key Concept l Logarithms with base b l Read: “Log of x base b is y”

Key Concepts l Common Logarithm: log 10 can just be written log • • l Log 100 is the same as log 10 100 There is a button on your calculator for log you can only use it when you are dealing with base 10! Natural Logarithm: loge is called the natural log and is written ln • • Loge 1 is the same as the ln 1 There is a button on your calculator for ln you can use this anytime you see ln in a problem!

Logarithmic to Exponential Form 1. log 6 216 = 3 2. log 4 1 = 0 3. log 3 81 = 4 4. ln e 2 = 2 5. log 40 = 1. 6

Exponential to Logarithmic Form 6. y = log 10 100 8. log 5 625 7. log 2 0. 25 = y 9. log 10 0. 001

Write each equation in logarithmic form 10. 29 = 512 12. e 5 =148. 4 11. 0. 04 -3/2 = 125

Evaluate Logarithmic Expressions 13. log 43 14. log 4300 15. ln 0. 05 16. log 2 32 17. log 5 1/125 18. log 11 1/121

Solve 19. logx 25 = 2 20. logx = 1/2 20. logx 9/100 = -2

Characteristics of Logarithmic Functions l l l 1. Inverse of the exponential function y=bx 2. Continous and one-to-one 3. Domain is all positive real numbers 4. y-axis is an asymptote 5. Range is ARN 6. Contains (1, 0), so x-intercept is 1

Helpful Hint l Since exponential and logarithmic functions are inverses if the bases are the same they “undo” each other…

Logarithmic Equations l Property of Equality • If b is a positive number other than 1, then if and only if x = y.

Example 4 l Solve

Example 5 l Solve

Example 6 l Solve

Example 7 l Solve

Example 8 l Solve

Example 9 l Solve

Example 10 l Solve

Example 11 l Solve