Formulas and properties of logarithms.
of number b
on the base a
) is defined as an exponent, in which it is necessary raise number a
to gain number b
(The logarithm exists only at positive numbers).
logab = x if and only if ax = b
The following types of logarithms are exist
- loga b - logarithm of number b on the base a (a > 0, a ≠ 1, b > 0)
- log b - common logarithms (Logarithms with base 10 are called common logarithms, a = 10).
- ln b - natural logarithms (Logarithms with base e are called natural logarithms, a = e).
Formulas and properties of logarithms
For any a
> 0; a
≠ 1 and any x
- alogab = b
- loga 1 = 0
- loga a = 1
- loga(x · y) = logax + logay
- loga xy = logax - logay
- loga 1x = -logax
- loga xp = p logax
- logak x = 1k loga x, for k ≠ 0
- logax = logac xc
- loga x = logb xlogb a - change of base formula
- loga x = 1logx a
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