Base, a mathematical term, refers to the power of n (x = n·m) or the logarithm of a (a(a>0 and a≠ 1) (x=logaN). For example, in the square of 9=3, the cardinal number is 3; 2 = In 2=log39, the radix is 3.
Natural alkali:
For the sequence {( 1+ 1/n) n}, when n tends to positive infinity, the limit of the sequence is e, that is, e = lim1+1/n) n.
Some properties of number e make it especially convenient as the radix of logarithmic system. Logarithms based on e are called natural logarithms. It is represented by a mark ln that does not mark the bottom; Natural logarithm is often used in theoretical research.
Sources of trona:
In history, natural logarithm was called Napier logarithm by mistake, and it was named after the inventor of logarithm-Scottish mathematician J. Napiera D.16-17. Napier himself has never had the concept of the base of logarithmic system, but his logarithm is equivalent to the logarithm whose base is close to 1/e, and Bilgi, his contemporaries, set a logarithm whose base is close to e.
Exponent is a power operation a? A parameter in (a≠0), where a is the base, n is the exponent, and the exponent is located in the upper right corner of the base. Power operation means the multiplication of the exponent base. When n is a positive integer, a? Represents n a multiplication. When n=0, a? = 1。
Development course:
The formation of the concepts of exponent and power is quite tortuous and slow. There are many symbols of power, and the symbols are diversified. There are at least ten different ways to write the word "right" in ancient China.
Liu Hui made a comment on the Nine Chapters of Arithmetic, and wrote in the rule of finding rectangular area in Square Field: "This product is called Tian Mi, and the product of multiplying the length and width of the square field is called power." This is the first time that power appears in mathematical literature.
When it comes to music, "Zhu Nanzi Astronomical Training" has the following words: "Therefore, the method of Huang Zhong is nine inches, which is a palace tune; So nine is nine and nine is eighty-one, so Huang Zhongzhi has the right to vote ... Twelve is thirty percent each, so one is eleven plus thirteen, which is 177,147. " The pipe that emits the rhythm of the yellow bell is 9 inches long, and its tone is called gong.