## Eduwhere's Concept: Logarithm

- Neha Gore
- last edited by

Questions on Logarithm have been asked in the CAT exam every year under the quantitative aptitude section. To solve logarithmic questions in CAT, logarithmic formulae are necessary.

Here is a set of important formulae you should know, take a quick look!

1. If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x

2. log a n is called logarithmic function. The domain of a logarithmic function is positive real numbers and the range is all real numbers.

3. log of 1 to any base is 0

log b 1 = 0

4. log of any number to base as itself is 1,

log a a = 1

5. Logarithm of a Product

log a pq = log a p + loga q

6. Logarithm of a Fraction

log a (p/q) = log a p – log a q

7. log a pn = n log a p

8. a(log a p) = p

9. Base Change Rule of Logarithms:

log a n = log b n × log a b

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11. if the base is 10, then

log a b = (log b)/(log a)

12. (log a b) × (log b a ) = 1

13. log a b = 1/log b a

14. log (m + n ) is not equal to log m + log n

15. log an p = 1/n (log a p)

16. log an bm = (m/n)log a b

17. log 10 b is called common logarithm because the base is 10

18. log e b is called natural logarithm. It is denoted by ln b.

19. log 1/a b = -log a b

20. log a (1/b) = -log a b

21. log 1/a (1/b) = log a b