Logarithms

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Important Formulas:


1.Let  and be positive real numbers with . The unique real number such that is called the Logarithm of to the base and is denoted as  . is not defined if .


2. Let


3.


4.


5. Logarithmic Function defined by is a positive real number is called a Logarithmic Function.


6. Logarithmic function is a bijection from


7.Types of Logarithms  to the base are called natural logarithms or Napierean logarithms and are written or instead of  Here


Properties of logarithms

8.


9. for any positive real number n.


10. here are positive real numbers.


11. If is a positive real number and is a real number then


12. Rule for change of base: If    and and is positive real number then


13. this gives


14.


15.


16.



17. Logarithmic series and exponential series: If then


18. Logarithmic series and exponential series: If then


19. Logarithmic series and exponential series: If then


20. is irrational and the value is approximately


21. (approx.)


22.


23.


24.