The log of high school mathematics and its related formulas

The knowledge points of high school mathematics are as follows:

1. Logarithmic formula.

If a x = n (a>0 and a ≠ 1), then x is called the logarithm of n with a as the base, denoted as x=log(a)(n), where a should be written at the bottom right of log. where a is called the base of the logarithm and n is called the true number.

2. We often call the logarithm with 10 as the base as the common logarithm, and the logarithm with e as the base as the natural logarithm.

3. The logarithmic formulas have loga(1)=0loga(a)=1, negative numbers and zeros have no logarithmic loga(mn)=logam+logan, loga(m n)=logam logan, and the n power of m in logam is nlogama (log(a)(b))=blog(a),(mn)=log(a)(m)+log(a)(n),log(a)(m n)=log(a)(m)- log(a)(n)，log(a)(m n)=nlog(a)(m)，log(a n)m=1 nlog(a)(m)。

log.

Derive steps. Let b=a m, a=c n, then b=(c n) m=c (mn).

Pair takes the logarithm of base a, which is: log(a)(b)=m

Take the logarithm based on c, which is: log(c)(b)=mn , and obtain: log(c)(b) log(a)(b)=n=log(c)(a) log(a)(b)=log(c)(b) log(c)(a).

log is the logarithm of high school math.

In general, the function y=logax(a>0, and a≠1) is called a logarithmic function, that is, a function with power (true number) as the independent variable, exponent as the dependent variable, and base number as a constant, which is called the logarithmic function.

Usually we call the logarithm with a base of 10 common logarithm and log10n as lgn. In addition, in science and technology, the logarithm of the irrational number e= is often used as the number of bottom sail dust.

The logarithm with e as the base is called the natural logarithm, and the logen is denoted as in n.

1. Basic knowledge

There is no logarithm between <> negative number and zero Qing quarrel.

2. Identities and proofs.

a^log(a)(n)=n (a>0 ，a≠1）。

Understanding and derivation of logarithmic formula operations by seeking rhyme in the world (8 photos).

Derivation: log(a) (a n) = n identity proof.

At a>0 and a≠1,n>0.

Let it be: when log(a)(n)=t, satisfies (t r).

then there is a t=n.

a^(log(a)(n))=a^t=n。

Logarithm is the operation of finding exponents, for example, log2x means finding the power of x is 2.

The monotonicity of logarithmic functions is divided into two categories by the magnitude relationship between the base a and 1: a>1, increasing, a<1, decreasing.

log2x 1=log2 2 (2 is the base, logarithm of 2).

So x<2, and the true number x>0.

So 0 x 2 .

So let's talk about the calculation of LG.

lg denotes the logarithm with a base of 10.

For example, the state difference Zen lgx=y, which is equivalent to 10 to the power of y=x.

Here are some formulas for calculating LG.

lga+lgb=lg(a*b) 。

lga-lgb=lg(a/b)。

In high school math, log (logarithm) is the mathematical relationship between exponents and logarithms. A logarithm is an exponent of a number (known as a true number) at a certain cardinal base, which can be expressed in the form of:

logₐ(x) =y

where a is the cardinal number (generally positive real number and not equal to 1), x is the true number (positive real number), and y is the exponent.

The definition of logarithm is the inverse of exponential operations. By solving for logarithms, we can get the solution for exponential operations.

2.Application of knowledge points:

In high school mathematics, the use of logarithms mainly includes the following aspects:

Properties and Algorithms of Logarithms: Understand the definition and basic properties of logarithms, including the inverse relationship between logarithms and exponents, and the operation rules of logarithms (such as the multiplication rules of logarithms, the division rules of logarithms, the power rule of logarithms, etc.).

Exponential and Logarithmic Functions: Understand the relationship between exponential and logarithmic functions, and master the properties, images, and transformations of exponential and logarithmic functions.

Application of logarithm in practical problems: In practical problems, logarithmic functions are often used to measure and describe the growth, decay, proportional relationship, and other phenomena of things.

3.Explanation of knowledge points and example questions:

Problem: Solve equation 3 x = 27.

Answer: This is an exponential equation that we can solve using the concept of logarithms.

Since exponential and logarithmic are inverse operations, we can convert the exponential equation into a logarithmic equation:

3 x = 27 can be written as log (27) =x

Based on the logarithmic definition, we can calculate the value of x: the unbridled branch.

log₃(27) =log₃(3^3) =3

So crack sensitive, the solution of equation 3 x = 27 is x = 3.

Through the above example explanation, we can understand that in high school mathematics, log (logarithm) is a mathematical concept used to express the relationship between exponents and logarithms. By defining and using numbers, we are able to solve equations and inequalities related to exponential and power functions.

Logarithm. In mathematics, logarithms are the inverse of exponentiation, just as division is the inverse of multiplication and vice versa. This means that the logarithm of one number is the exponent that must produce another fixed number (cardinal fuqing).

In the simple case, the multiplier counts the factor in the pair of great god numbers. More generally, exponentiation allows any positive real number to be raised to any real power that is lost to any roller, always yielding a positive result, so that the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1.

If a to the power of x is equal to n(a>0 and a ≠ 1), then the number x is called logarithm with a as the base n, denoted as x=loga n. where a is called the base of the logarithm and n is called the true number.

1.Quadratic Functions and Images: Definition of quadratic functions, properties of images, translation, scaling, etc.

2.Inequalities and Linear Programming: Inequalities and Linear Programming: Inequalities, Inequalities, Linear Programming, Concepts and Solutions.

3.Trigonometric functions: definitions, properties, images, basic relations, calculation of special angles, etc.

4.Planar vectors: definitions, operations, quantity products, collinear and perpendicular concepts of vectors.

5.Probability and Statistics: Basic concepts of probability, calculation of events, basic concepts of statistics, analysis and representation of crack data, etc.

6.Applications of derivatives and functions: definition, properties, derivatives, extremums of functions, maximums, drawing of images, etc.

7.Matrices and determinants: the definition of matrices, operations, definition and properties of determinants, solving systems of linear equations, etc.

8.Trigonometric identity transformation: the basic relations of trigonometric functions, the proof and application of trigonometric identities.

9.Spatial analytic geometry: spatial coordinate systems, points, lines, properties of planes, intersecting relationships, distances, angles, etc.

10.Number series and mathematical induction: the concept of number series, equal difference number series, the properties of proportional number series, summation formula, application of mathematical induction, etc.

One is the definition and operation of logarithms, the second is the image and properties of logarithmic functions, and the third is logarithms and applications.

For y=logab, then a is the bottom of the logarithmic number, b is the true number, where a is a positive number, and not 1, and b is a positive number.

Definition of logarithms, logarithmic identities, four rules of operation for logarithms, images and properties of logarithmic functions, etc.

Definition of logarithms, properties of operation formulas and basic operations.

The formula for high school math log: log(a)(mn) = log(a)(m) + log(a)(n). Standard Language Expressions YesIf a=b(a>0 and a≠1) then n=logab and if a n=b(a>0 and a≠1) then n=log(a b).

Multiply and divide into addition and subtraction", so as to achieve the idea of simplifying the calculation, is not the obvious feature of logarithmic operations. Napier's method of calculation is actually completely in modern mathematics"Logarithmic operations"thoughts.

Property analysis. log, the symbolic English for logarithms, is an abbreviation of the noun logarithms. Logarithmic operations are defined as follows:

If a=b(a>0 and a≠1) then n=logab. Of these, a is called"Base", b is called"True numbers", n called"The logarithm of b with a base of a"。There is no logarithm for zero and negative numbers.

When the base number is not written, 10 is generally used as the base number by default.

The relationship between these two rows of numbers is very clear: the first row represents the exponent of 2, and the second row represents the corresponding power of 2. If we want to calculate the product of two numbers in the second row, we can do so by adding the corresponding numbers in the first row.

There is no substantial conversion between the two. BaseWhen 10 is abbreviated as lg, log10 = lg.

When the base number is e, Hu Song is abbreviated as ln, logex=lnx.

Brief introduction. log logarithm.

In mathematics, logarithms are the inverse of power, just as division is the reciprocal of multiplication and vice versa. Trouser pure means that the logarithm of one number is the exponent that must produce another fixed number (cardinality).

In the simple case, the logarithmic count factor in the multiplier. More generally, exponentiation allows any positive real number to be cast.

Increasing to any real power always yields a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1.

The algorithm of the log formula in high school is: loga(mn)=logam+logan; loga（m/n）=logam-logan；logann=nlogan，（n，m，n∈r）。If a=em, then m is the natural logarithm of the number a, i.e., LNA=M, and E= is the base of the natural logarithm.

It is an infinite non-cyclic decimal.

Logarithmic formula. It is a common formula in mathematics, if a x = n (a>0, and a ≠ 1), then x is called the logarithm of n with a as the base, which is denoted as x=log(a)(n), where a should be written under the log right imitation. where a is called the base of the logarithm and n is called the true number.

Usually the logarithm with a base of 10 is called a common logarithm, and the good number with a base of e is called a natural logarithm.

1. Generally refers to logarithms.

2.In mathematics, logarithm is the inverse of exponentiation, just as division is the reciprocal of multiplication, and vice versa. This means that the logarithm of one number is the exponent that must produce another fixed number (cardinality).

In the simple case, the logarithmic travel key in the multiplier counts the factor. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1.

3.If the power of x of a is equal to n(a>0 and a ≠1), then the number x is called the logarithm of n with a as the base, and is denoted as x=logan. where a is called the base of the logarithm and n is called the true number.

2. The relationship between the logarithmic function and the exponent:

The logarithmic function of the same base is inverse to the exponential function. When a>0 and a≠1, ax=n, x=an. About y=x symmetry.

The general form of the logarithmic function is y=ax, which is actually the inverse of the exponential function (the two functions of the image about the symmetry of y=x on the straight line of Lu Zhenzi are inverse functions of each other), which can be expressed as x=ay. Therefore, for the exponential function for a (a>0 and a≠1), the figure on the right gives the graph of the function represented by the different magnitudes a: with respect to the x-axis symmetry, when a > 1, the larger a, the closer the image is to the x-axis, and when 0 <>