### MCQ's collected from all Engineering Entrance Examinations (Click here)

### 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.