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Mastering Logarithmic Functions: Definitions and Examples

Learn the fundamentals of logarithmic functions and their inverses with detailed explanations, examples, and practice problems. Explore the relationship between logarithmic and exponential functions.

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Mastering Logarithmic Functions: Definitions and Examples

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  1. 8.3 Logarithmic Functions and Inverses

  2. A logarithm is an exponent! Definition: If y = bx then logby = x b CANNOT = 1 & b > 0

  3. Ex 1 Write in logarithmic form: 32 = 25

  4. Ex 2 Write in logarithmic form:

  5. Ex 3 Solve: log381

  6. Ex 4 Solve: log927

  7. Ex 5 Solve: log64

  8. Common logarithm • A log that uses base 10 • log10y or log y (understood base 10)

  9. A log function is the inverse of an exponential function.

  10. Ex 6 Graph: y = 4x and y = log4x

  11. Ex 7 Find the inverse: y = log7x

  12. Ex 8 Find the inverse: y = log55x

  13. Ex 9 Find the inverse: y = log3x4

  14. Ex 10 • log4n=

  15. Ex 11

  16. Ex 12 • logb9 = 2

  17. Ex 13

  18. Ex 14

  19. Ex 15 • log557 = x

  20. Ex 16

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