- if n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x
- log a n is called logarithmic function. The domain of a logarithmic function is positive real numbers and the range is all real numbers.
- log of 1 to any base is 0
*log b 1 = 0*
- log of any number to base as itself is 1,
*log a a = 1*
- The logarithm of a Product log a
*pq = log a p + loga q*
- The logarithm of a Fraction log a
* (p/q) = log a p – log a q*
- log a
*pn = n log a p*
- a(log a p) = p
- Base Change Rule of Logarithms:
*log a n = log b n × log a b*
- log a b = (log nb)/(log n a)
- if the base is 10, then
*log a b = (log b)/(log a)*
*(log a b) × (log b a ) = 1*
*log a b = 1/log b a*
*log (m + n ) is not equal to log m + log n*
*log an p = 1/n (log a p)*
*log an bm = (m/n)log a b*
- log 10 b is called common logarithm because the base is 10
- log e b is called natural logarithm. It is denoted by ln b.
*log 1/a b = -log a b*
*log a (1/b) = -log a b*
*log 1/a (1/b) = log a b*