Exponents and Logarithms 指數和對數

04-25

What is a logarithm?

Logarithms are another way of thinking about exponents.

If we know that 2 raised to the 4th power equals 16, well express it by the exponential equation $2^{4} = 16$ . If we asked 「2 raised to which power equals 16?」, the answer would be 4. This is expressed by the logarithmic equation $log_{2}{16} = 4$ , read as 「log base two of sixteen is four.」

$2^{4} = 16 ; Longleftrightarrow ; log_{2}{16} = 4$

Both equations describe the same relationship between the numbers 2, 4, and 16, where 2 is the base and 4 is the exponent. The difference is that while the exponential form isolates (使脫離,孤立) the power, 16, the logarithmic form isolates the exponent, 4.

Definition of a logarithm

$b^{a} = c ; Longleftrightarrow ; log_{b}{c} = a$

Both equations describe the same relationship between a, b, and c:

b is the base (底數),
c is the exponent (指數), and
a is called the argument (函數的自變數).