Grade 11: General Mathematics: Logarithms
- 1. INTRODUCTION TO LOGARITHM ANNALYN MANIEGO CABATINGAN
- 2. LEARNING OBJECTIVES After going through this module, you are expected to: 1. Rewrite exponential equations to logarithmic form and vice versa 2. Distinguishes logarithmic functions, logarithmic equations, and logarithmic inequalities
- 3. Find the value of x. ACTIVITY 1: 8)50
- 4. LOGARITHM 01 - is the power to which a base must be raised to produce a given number. 𝒃𝒄 =𝒂 log𝒃 𝒂=𝒄 Exponential form Logarithmic form
- 5. SPECIAL LOGARITHMS COMMON LOGARITHMS are logarithms with base 10 NATURAL LOGARITHMS are logarithms with base e
- 6. Rewrite the following exponential equations in logarithmic form. ACTIVITY 2:
- 8. A. Rewrite the following logarithmic equations in exponential form. ASSIGNMENT: B. Rewrite the following exponential equations in logarithmic form.
- 10. LOGARITHMIC EQUATION LOGARITHMIC INEQUALITY LOGARITHMIC FUNCTION Definition An equation involving logarithms. An inequality involving logarithms. Function of the form Example
- 11. C. Determine whether the given is a logarithmic function, logarithmic equation, a logarithmic inequality or neither. ASSIGNMENT:
- 13. EXPLORATION: Directions: Find the value of the following.
- 14. BASIC PROPERTIES OF LOGARITHMS Let b and x be real numbers such that and , the basic properties of logarithms are as follows: • , then ¿ 𝟎 ¿ 𝐱 ¿ 𝐱
- 15. Use the basic properties of logarithms to find the value of the following logarithmic expressions. ACTIVITY 1:
- 16. Use the basic properties of logarithms to find the value of the following logarithmic expressions. SEATWORK:
- 17. A. Use the properties of logarithm to find the value of the following given. MODULAR DISTANCE LEARNING
- 18. A. Use the properties of logarithm to find the value of the following given. MODULAR DISTANCE LEARNING 2
- 20. EXPLORATION: Directions: Find the value of the following.
- 21. LAWS OF LOGARITHMS Let , and let . For , , then 𝐥𝐨𝐠𝐛(𝒖𝒗)
- 22. EXPLORATION: Directions: Find the value of the following.
- 23. LAWS OF LOGARITHMS Let , and let . For , , then
- 24. EXPLORATION: Directions: Find the value of the following.
- 25. LAWS OF LOGARITHMS Let , and let . For , , then
- 26. CHANGE-OF-BASE FORMULA Any logarithmic expression can be expressed as quotient of two logarithmic expressions with a common base. Let a, b, and x be positive real numbers, with a 1, b 1:
- 27. A. Use the laws of logarithms to expand the expressions as sum, difference or multiple of logarithms. ASSIGNMENT:
- 28. B. Use the laws of logarithms to condense the expressions as a single logarithm. ASSIGNMENT:
- 29. C. Use of change-of-base formula to rewrite the following logarithmic expressions to the indicated bases. ASSIGNMENT: 1) (change to base 2) 2) (change to base 5)
- 30. A. Use the laws of logarithms to expand the expressions as sum, difference or multiple of logarithms. SEATWORK:
- 31. B. Use the laws of logarithms to condense the expressions as a single logarithm. SEATWORK:
- 32. C. Use of change-of-base formula to rewrite the following logarithmic expressions to the indicated bases. SEATWORK: 𝐥𝐨𝐠𝟑𝟖𝟏(change to base 9)
- 34. TECHNIQUES: 1. Rewriting to exponential form 2. Applying the one-to-one property of logarithmic functions If , then . 3. Using logarithmic properties and laws 4. The Zero Factor Property: If , then or .
- 35. Exercises: Solve the following logarithmic equations.
- 36. Exercises: Solve the following logarithmic equations.
- 37. Exercises: Solve the following logarithmic equations.
- 38. ASSIGNMENT PREPARE FOR INDIVIDUAL PERFORMANCE TASK NEXT WEEK. Coverage: EXPONENTIAL AND LOGARITHMIC FUCTIONS, EQUATIONS, AND INEQUALITIES
- 39. If you don’t play by the rule, don’t complain if you lose.