Logarithms Formula

  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