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:
- 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
- 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
- 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
- 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
- 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
- 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
- Problem 6: Summation using multiplication law
- Given: log base 10 of 7, log base 10 of 2
- Find: log base 10 of 14
- Problem 7: Simplification using multiplication law
- Given: log base 7 of 343
- Find: log base 7 of 7
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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: