For students, learning high school mathematics must go through the following four steps:

1. Understand concepts (nouns, definitions, connotations, extensions),

2. Master relationships (rules, formulas, theorems, laws),

3. Flexible use (identification, discrimination, type, question type),

4. Forming ability (calculation, analysis, induction and synthesis). Comprise a logarithmic function.

The following uses "logarithm" (excluding logarithmic function) to reveal the learning process:

1. Understand the concept of logarithm.

(1) introduces the term logarithm.

In Equation 2? =8, change 2? X in =x is a power operation, so what about X? X in =8 is the root operation,

Finding x in 2 x = 8 is a logarithmic operation. That is, an index with 2 as the base and 8 as the power, which is called logarithm for short.

(2) Describe the definition of logarithm.

In exponential formula a, b = n(a >；; 0, and a≠ 1), where b is called the base of a, and the exponent of n is symbolically expressed as b = Logan (a >; 0, and a≠ 1, n >；; 0)。 In the logarithmic formula, a is called the base (radix) and n is called the real number. Real numbers and power.

(3) Understand the connotation of logarithmic concept. Common logarithm log 10N=lgN, natural logarithm logeN=lnN,

Lg 1 = 0，ln 1=0 = 0，Lg 10 = 1，LNE = 1。 Logarithm generally refers to ordinary logarithm.

(4) Understanding the extension of logarithmic concept. Conversion between exponential expression and logarithmic expression; Form y= logax (0

2. Master the logarithmic operation relationship.

(1) Deduce the logarithmic operation rule.

①loga(MN)= logaM+logaN； ②loga(M/N)= logaM-logaN；

③ logam n = enrogam; ④loga n√M= ( 1/n)logaM .

(2) Prove the logarithmic operation formula.

Logarithmic identity: a Logan = n, elnn = n;

The bottom change formula: logab = (logcb)/(logca) = (LGB)/(LGA) = (LNB)/(LNA).

3. Flexible use of logarithm.

Identification of (1) logarithm. ①lg2+lg5 = _ _ _ _； ②lg4+lg25 = _ _ _ _ _ _ _；

③ Solve equation y=log(x? - 1)(3x+ 1)= 1； ④ Find the function y=log(x- 1)(-x? +2x+3)。

(2) Discrimination of logarithm. ① loga2 = m，loga 3=n，a 2m+n；

② If the coordinate of point P(lga, lgb) about the axisymmetric point is (1, -2), find the value of loga b.

(3) the type of logarithm. Logarithm, then logarithmic function. Logarithmic function, exponential function, power function and quadratic function are all basic elementary functions. So logarithm is conceptual knowledge, so we must learn it well.

(4) logarithmic problems. ① Concept discrimination; ② Logarithmic calculation; ③ Solving logarithmic equation; ④ Solving problems by logarithmic method.

4. The ability to form logarithm.

(1) logarithmic calculation ability. ① Given lg2=a and lg3=b, find lg√45 (expressed by algebra containing A and B);

② Given that log 14 7=a, 14 B = 5, find log35 28 (represented by algebra containing a and b).

(2) Logarithmic analysis ability. ① compare log0.2 0.3, log0.3 0.2 and ln(e? +1) size;

② Find the inverse function of function y = ln [(x+1)/(x-1)] and y=log2[√(x+4)+2].

(3) Logarithmic induction ability. ① Compare the sizes of 2 100 and 10 30 by logarithmic method (known as LG2 = 0.3010);

② Is the quadratic function f(x)=(lga)x known? The maximum value of +2x+4lga is 3. Find the value of a ..

(4) Logarithmic comprehensive ability. ① Given f (x 6) = logax, find the value of f (16);

② f(x)=log( 1/3) (x？ The value range of +mx+2) is r, and the value range of real number m.

After reading it, do you think people who have studied math for two hours for the first time can finish it and learn it well? Tutoring in this school is a must!

I hope it inspires you. Good wishes!