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

Usually, we call the logarithm with 10 as the common logarithm, and record log 10N as lgN. In addition, the logarithm of irrational number e = 2.7 1828 ... is often used in science and technology.

Logarithm based on e is called natural logarithm, and logeN is recorded as in n.

1, basic knowledge

①

②

③ There is no logarithm between negative number and zero.

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2. Identity and its proof.

a^log(a)(n)=n(a & gt； 0，a≠ 1)。

Understanding and deducing logarithmic formula operation by finding rhyme in the world (8 sheets)

Deduction: Prove the identity of log (a) (an n) = n.

At a>0 and a≠ 1, n >；; At 0 o'clock.

Let: when log(a)(N)=t, (t∈R) is satisfied.

Then there is a t = n.

a^(log(a)(N))=a^t=N。

Logarithm is an exponential operation, for example, log2x is how many times x is 2.

Monotonicity of logarithmic function can be divided into two categories according to the relationship between base a and 1: A >；; 1, increasing, a

Log2x < 1 = log22 (2 is the base and logarithm of 2).

So x < 2, real number x>0.

So 0 < x < 2.

Let me talk about lg's calculation. ?

Lg stands for logarithm with base 10. ?

For example, lgx=y, which is equivalent to y = X power of 10.

Here are some formulas for calculating lg.

lgA+lgB=lg(A*B).

lgA-lgB=lg(A/B).