Antilogarithm

Antilogarithm is a slang term for the exponential function on base 10.

If a multiplication or division is carried out with the help of log tables , the logarithms of the factors are added or the logarithms of the dividend and divisor are subtracted. The result is then obtained by "antilogarithmizing". Other terms for "antilogarithm" are "delogarithm", "de-logarithm" and "exponentiate".

The slide rule is based on this principle .

Sample calculation

The division 12345678 by 23456 is to be carried out. First we log to base 10 which gives us 7.0915 and 4.3703. The subtraction gives 2.7212, using the antilogarithm we get the result 526.3.

Derivation

Multiplication:

${\displaystyle x\cdot y=a^{\log _{a}\!x}\cdot a^{\log _{a}\!y}=a^{\log _{a}\!x+\log _{a}\!y}}$

Division:

${\displaystyle {\frac {x}{y}}={\frac {a^{\log _{a}\!x}}{a^{\log _{a}\!y}}}=a^{\log _{a}\!x-\log _{a}\!y}}$

literature

• Antilogarithm . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).