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Logarithmic Functions TS:Making Decisions After Reflection and Review

Learn how to write exponential equations in logarithmic form, expand and condense logarithmic expressions, and solve logarithmic and exponential equations. Discover the properties of logarithms and delve into evaluating special bases like common and natural logarithms.

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Logarithmic Functions TS:Making Decisions After Reflection and Review

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  1. Logarithmic Functions TS:Making Decisions After Reflection and Review

  2. Objectives • To write exponential equations in logarithmic form. • To use properties of logarithms to expand and condense logarithmic expressions.

  3. Logarithmic Functions • Key to understanding logarithms: A logarithm is an exponent! Exponent Base Argument It is asking: “What power would I take b to in order to get a?”

  4. Logarithmic Functions

  5. Logarithmic Functions • Evaluate:

  6. Logarithmic Functions • Evaluate:

  7. Logarithmic Functions • Evaluate:

  8. Logarithmic Functions • Evaluate:

  9. Logarithmic Functions • Evaluate:

  10. Logarithmic Functions • Evaluate:

  11. Logarithmic Functions • Evaluate:

  12. Special Bases Common log Natural log

  13. Natural Logarithm • Evaluate:

  14. Properties of Logarithms

  15. Properties of Logarithms • Expand:

  16. Properties of Logarithms • Expand: ln does not distribute!

  17. Properties of Logarithms • Expand:

  18. Properties of Logarithms • Expand:

  19. Conclusion • A logarithm indicates the exponent to which you raise a certain base in order to produce a given value. • The inverse of logarithmic function is an exponential function. • Logs to the base 10 are written without a base. • Logs to the base e are indicated by the symbol ln.

  20. Begin your HW –Day 7 p.283 #1-8, 23-39 Apply the inverse properties of logarithmic and exponential functions to simplify. 23) 24) 25) 26) 27) 28) Re-write the logarithmic equation as an exponential equation, or vise versa. 1) 2) 3) 4) 5) 6) 7) 8)

  21. Logarithmic FunctionsDay 2TS:Making Decisions After Reflection and Review

  22. Objectives • To use properties of logarithms to expand and condense logarithmic expressions. • To be able to solve logarithmic and exponential equations

  23. Properties of Logarithms

  24. Properties of Logarithms • Combine:

  25. Properties of Logarithms • Combine:

  26. Properties of Logarithms • Combine:

  27. Properties of Logarithms • Combine:

  28. Properties of Logarithms • Combine:

  29. Solve: Solve: Logarithmic Functions

  30. Solve: Solve: Logarithmic Functions

  31. Solve: Solve: Logarithmic Functions

  32. Solve: Solve: Logarithmic Functions

  33. Logarithmic Functions • Suppose you deposit money into an account whose annual interest rate is 4% compounded continuously. How long will it take for the money to double?

  34. Conclusion • A logarithm indicates the exponent to which you raise a certain base in order to produce a given value. • The inverse of logarithmic function is an exponential function. • Logs to the base 10 are written without a base. • Logs to the base e are indicated by the symbol ln.

  35. Begin your HW –Day 8 p.284 #41-63,67, 71-77odd Solve for x or t. 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) Write as a single logarithm. 41) 42) 43) 44) 45) 46) 47) 48) 49) 50)

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