Logarithm - 2 Problem on Summation (Change of Base & Multiplication Law)

• Review of logarithm
• Problem 1: Summation using change of base
  • Given: log base 3 of 9, log base 2 of 9, log base 5 of 9
  • Find: log base 6 of 9
• Problem 2: Summation using multiplication law
  • Given: log base 7 of 5, log base 7 of 3
  • Find: log base 7 of 15
• Problem 3: Simplification using multiplication law
  • Given: log base 4 of 81
  • Find: log base 4 of 3
• Problem 4: Simplification using logarithmic identities
  • Given: log base 5 of 5^4 - log base 5 of 5^2
  • Find: log base 5 of 625
• Summary of key points so far

The requested slides 11 to 20 are as follows:

11. Solution of Problem 1: Summation using change of base
    • log base 3 of 9 = log base 10 of 9 / log base 10 of 3
    • log base 2 of 9 = log base 10 of 9 / log base 10 of 2
    • log base 5 of 9 = log base 10 of 9 / log base 10 of 5
    • log base 6 of 9 = log base 10 of 9 / log base 10 of 6
    • Substitute the given values into the equation
    • Simplify the expression to find the value of log base 6 of 9

12. Solution of Problem 2: Summation using multiplication law
    • log base 7 of 5 = log base 7 of 3 * log base 3 of 5
    • Given, log base 3 of 5
    • Substitute the given values into the equation
    • Simplify the expression to find the value of log base 7 of 15

13. Solution of Problem 3: Simplification using multiplication law
    • log base 4 of 81 = 4 * log base 4 of 3
    • Given, log base 4 of 81
    • Substitute the given value into the equation
    • Simplify the expression to find the value of log base 4 of 3

14. Solution of Problem 4: Simplification using logarithmic identities
    • log base 5 of 5^4 - log base 5 of 5^2 = 4 - 2
    • Simplify the expression to find the value of log base 5 of 625

15. Summary of key points so far
    • Logarithm can be solved using change of base and multiplication law
    • Change of base formula: log base a of b = log base c of b / log base c of a
    • Multiplication law: log base a of b * log base b of c = log base a of c
    • Logarithmic identities can be used to simplify expressions
    • Examples of solving problems using these techniques

16. Problem 5: Summation using change of base
    • Given: log base 2 of 16, log base 3 of 16, log base 4 of 16
    • Find: log base 5 of 16

17. Problem 6: Summation using multiplication law
    • Given: log base 10 of 7, log base 10 of 2
    • Find: log base 10 of 14

18. Problem 7: Simplification using multiplication law
    • Given: log base 7 of 343
    • Find: log base 7 of 7

19. Problem 8: Simplification using logarithmic identities
    • Given: log base 6 of 6^3 - log base 6 of 6^2
    • Find: log base 6 of 6^5

20. Summary of problem-solving techniques
    • Recap of change of base and multiplication law
    • Examples of solving problems using these techniques
    • Importance of simplification using logarithmic identities
    • Review of key points covered in the lecture

21. Problem 5: Summation using change of base
    • Given: log base 2 of 16, log base 3 of 16, log base 4 of 16
    • Find: log base 5 of 16
    • Substitute the given values into the change of base formula
    • Simplify the expression to find the value of log base 5 of 16

22. Solution of Problem 5: Summation using change of base
    • log base 2 of 16 = log base 10 of 16 / log base 10 of 2
    • log base 3 of 16 = log base 10 of 16 / log base 10 of 3
    • log base 4 of 16 = log base 10 of 16 / log base 10 of 4
    • log base 5 of 16 = log base 10 of 16 / log base 10 of 5
    • Substitute the given values into the equation
    • Simplify the expression to find the value of log base 5 of 16

23. Problem 6: Summation using multiplication law
    • Given: log base 10 of 7, log base 10 of 2
    • Find: log base 10 of 14
    • Use the multiplication law to solve the problem
    • Simplify the expression to find the value of log base 10 of 14

24. Solution of Problem 6: Summation using multiplication law
    • log base 10 of 7 * log base 10 of 2 = log base 10 of 14
    • Substitute the given values into the equation
    • Simplify the expression to find the value of log base 10 of 14

25. Problem 7: Simplification using multiplication law
    • Given: log base 7 of 343
    • Find: log base 7 of 7
    • Use the multiplication law to simplify the expression
    • Simplify the expression to find the value of log base 7 of 7

26. Solution of Problem 7: Simplification using multiplication law
    • log base 7 of 343 = 3 * log base 7 of 7
    • Substitute the given value into the equation
    • Simplify the expression to find the value of log base 7 of 7

27. Problem 8: Simplification using logarithmic identities
    • Given: log base 6 of 6^3 - log base 6 of 6^2
    • Find: log base 6 of 6^5
    • Use logarithmic identities to simplify the expression
    • Simplify the expression to find the value of log base 6 of 6^5

28. Solution of Problem 8: Simplification using logarithmic identities
    • log base 6 of 6^3 - log base 6 of 6^2 = 3 - 2
    • Simplify the expression to find the value of log base 6 of 6^5

29. Summary of problem-solving techniques
    • Recap of change of base and multiplication law
    • Examples of solving problems using these techniques
    • Importance of simplification using logarithmic identities
    • Review of key points covered in the lecture

30. Review and Conclusion
    • Recap of the topics covered in the lecture
    • Importance of understanding logarithm and its applications
    • Practice and application of problem-solving techniques
    • Encouragement for further study and exploration of logarithm
    • Q&A session and closing remarks