e = 2.7182.... - e constant or Euler's number
Base e logarithm of x can be expressed as
log e (x) = ln (x) = y
|System||Log to the base of||Terminology|
|log a||a||log to base a|
|log 10 = lg||10||common log|
|log e = ln||e = 2.718281828459..||natural log|
|log 2 = lb||2||log to base 2|
log a (x y) = log a (x) + log a (y) (2)
log a (x / y) = log a (x) - log a (y) (3)
log a (x p ) = p log a (x) (4)
log a (1 / x) = - log a (x) (5)
log a (b) = 1 (6)
log a (1) = 0 (7)
log a (0) = undefined (8)
log a (x < 0) = undefined (9)
log a (x) = log c (x) / log c (a) (10)
log a (x → ∞) = ∞ (11)
log 10 ((5) (6)) = log 10 (5) + log 10 (6)
= 0.6990 + 0.7782
lg (x) = lg (e) ln (x)
= 0.434294 ln (x) (12)
ln (x) = lg (x) / lg (e)
= 2.302585 lg (x) (13)
lb (x) = 1.442695 ln (x)
= 3.321928 lg (x) (15)
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