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. The logarithm of a Product log a pq = log a p + loga q
6. The 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
10. log a b = (log nb)/(log n a)
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