Any numeral is known as a number. Numbers are of various types. Let us discuss the types of numbers.

- Definition: a
^{x}= b can be represented in logarithmic form as log_{a}b = x - log a = x means that 10
^{x}= a . - 10
^{log a}= a (The basic logarithmic identity). - log (ab) = log a + log b, a > 0, b > 0
- log(a/b) = log a -log b, a > 0, b > 0.
- log a
^{n}= n (log a) (Logarithm of a power). - log
_{x}y = log_{m}y / log_{m}x (Change of base rule). - log
_{x}y = 1 / log_{y}x . - log
_{x}1 = 0 (x ≠ 0, 1). - The natural numbers 1, 2, 3,.... are respectively the logarithms of 10, 100, 1000, .... to the base 10.
- The logarithm of "0" and negative numbers are not defined.
- log
_{b}1= 0 (∵ b^{0}= 1) - log
_{b}b = 1 (∵ b_{1}= b) - y = ln x → e
^{y}= x - x = e
^{y}= → ln x = y - x = ln e
^{x}= e^{ln x} - e
^{logbx}= x - log
_{b}b^{y}= y

- log
_{b}MN = log_{b}M + log_{b}N (where b, M and N are positive real numbers and b ≠ 1) - log
_{b}(M/N) = log_{b}M - log_{b}N (where b, M and N are positive real numbers and b ≠ 1) - log
_{b}(M^{c }) = c log_{b}M (where b, M and N are positive real numbers and b ≠ 1 and c is any real number) - log
_{b}M = logM/logb = lnM/lnb = log_{k}M/log_{k}b (where b, M and k are positive real numbers and b ≠ 1, k≠1) - log
_{b}a = 1/log_{a}b (where b, and a are positive real numbers and b ≠ 1, a≠1) - If log
_{b}M = log_{b}N, then M = N (where b, M and N are positive real numbers and b ≠ 1)

A mathematical consonant e is the base of the natural logarithm, known as Euler's number. It is also known as Napier's consonant.