Nature:

1, the definition of logarithm: For positive number A and real number X greater than 0, the logarithm of X based on A is expressed as log? (x), that is, the power of a is equal to x, such as log? (8) = 3 because of 2? = 8。

2. For any positive number A, log? (a) = 1, that is, the logarithm of a to a is equal to 1.

3. For any positive number A, log? (1) = 0, that is, the logarithm of 1 based on a is equal to 0.

4. For any positive number A, log? (a^b) = b, that is, the logarithm of the b power with a as the base is equal to B.

Algorithm:

1, logarithmic multiplication rule: log? (xy) = log？ (x) + log？ (y). That is to say, the logarithm of the product of two numbers is equal to the sum of the logarithms of these two numbers. Like log? (4 × 8) = log？ (4) + log？ (8) = 2 + 3 = 5。

2. Logarithmic division rule: log? (x/y) = log？ (x) - log？ (y). That is, the logarithm of the quotient of two numbers is equal to the difference between the two numbers after the logarithm. Like log? (27/3) = log？ (27)-Log? (3) = 3 - 1 = 2。

3. logarithmic power law: log? (x^b) = b × log？ That is to say, the logarithm of the power of a number is equal to the product of the logarithm and exponent of the number. Like log? (2? )= 2 × log？ (2)。

4. Bottom changing formula: log? (x) = log？ (x) / log？ (A) Fifty percent. That is, the logarithm of a number can be expressed by the logarithm of different bases, and the logarithm can be converted into other bases by this formula.

Matters needing attention of attributes and algorithms

1. In mathematics, a property is a statement describing the characteristics of an object or set, such as commutative law and associative law. Arithmetic refers to the rules that need to be followed when performing operations.

2. Different mathematical objects have different properties and algorithms. For example, addition on a set of real numbers satisfies the commutative law and associative law, and multiplication also satisfies the distributive law.

3. Familiarity with properties and algorithms can help us solve problems quickly and understand mathematical concepts. Therefore, when learning mathematics, we need to master the properties and algorithms of different mathematical objects carefully.