Logarithmic operations. The more detailed, the better.

Solution: Logarithmic base formula.

Solution: From log[c]a=(1 log[a]c), we get (1)log[a]c log[c]a=1

2）log[2]3•log[3]4•log[4]5•log[5]2

1/log[3]2)•2log[3]2•(1/2log[5]2)•log[5]2

3）（log[4]3+log[8]3）（log[3]2+log[9]2）

1/log[3]4)+(1/log[3]8)）（1/log[2]3)+(1/log[2]9)）

1/2log[3]2)+(1/3log[3]2)）（1/log[2]3)+(1/2log[2]3)）

5/6log[3]2)•(3/2log[2]3)

The third question is the formula lg(3) lg(2)*lg(4) lg(3)*lg(5) lg(4)*lg(2) lg(5)=1

Question 4: A little comprehensive operation plus partial bottom change (1 2log2(3)+1 3log2(3))(log3(2)+1 2log3(2))=5 6log2(3)*3 2log3(2)=5 4

Feel free to ask

1. The corresponding calculation method of LN is as follows:

1) The logarithm of the product of two positive numbers is equal to the sum of the logarithms of the two numbers of the same base, i.e.:

(2) The logarithm of two positive quotients is equal to the difference between the logarithm of the dividend-received number and the logarithm of the divisor of the same base, i.e.:

(3) The logarithm of a positive power is equal to the logarithm of the base of the power multiplied by the exponential of the power, i.e.,

(4) If the power exponent in the equation then there is the following logarithmic operation rule of the arithmetic root of a positive number: the logarithm of the arithmetic root of a positive number is equal to the logarithm of the square number divided by the root exponent, i.e.:

The natural logarithm is the logarithm of the base of the constant e, denoted as lnn(n>0). It is also common in mathematics to use logx to represent natural logarithms, so the calculation of lnx can also be done using the above formula.

2. LN2-LN1 is obtained by using the above equation (2): LN2-LN1=LN2(2 1)=LN2.

There's nothing wrong with that.

lg81)/2=(2lg9)/2=lg9

Know that (lg81) 2 and lg(81 2) are completely different.

Is it understandable that lg81 = lg9 square = 2lg9? 2 The appointment is gone.

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 count factor in the multiplier.

More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive delayed calendar result, so 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.

If a(a>0, and a≠1) to the power of b is equal to n, i.e., ab=n, then the number b is called the logarithm of a base n, denoted as: logan=b, where a is called the base of the logarithm, and n is called the true number of the file grip.

By definition: the manuscript is stupid.

There is no logarithm for negative and zero;

a>0 and a≠1,n>0;

loga1=0，logaa=1，alogan=n，logaab=b。

Logarithmic arithmetic:

1、log(a) (m·n）=log(a) m+log(a) n

2、log(a) (m÷n)=log(a) m-log(a) n

3、log(a) m^n=nlog(a) m

4. Key disturbance log(a)b*log(b)a=1

5、log(a) b=log (c) b÷log (c) a

Algorithm of Exponents:

1. [a m] [a n]=a (m n) [multiply with the power of the base, the base does not change, and the exponent is added].

2. [a m] [a n]=a (m n) [divide by the power of the same base, the base does not change, and the exponent is subtracted].

3. [a m] n=a (mn) [power of power, base unchanged, exponential multiplication].

4. [ab] m=(a m) (a m) [the power of the product, equal to the multiplication of each factor, and then multiply the resulting powers].

Addition formula: the sum of the logarithms of these two numbers of the same base is equal to the logarithm of the product of two positive numbers;

Subtraction formula: the logarithm of the dividend of the same base is equal to the logarithm of the quotient of two positive numbers.

Summary. Rule of logarithmic operations is a special method of operation. Refers to the operation rules of the logarithm of the product, quotient, power, and square root.

From the mutual conversion relationship between exponents and logarithms, it can be obtained: 1The logarithm of the product of two positive numbers is equal to the sum of the logarithms of the two numbers of the same base, i.e.:

2.The logarithm of two positive quotients, equal to the logarithm of the dividend-bound of the same base minus the difference between the logarithms of the dividend, i.e.: 3

Bottom change formula. Rule of logarithmic operations is a special method of operation. Refers to the arithmology of the product, quotient, power of annihilation, and logarithm of the square root. From the mutual exponential and logarithmic transformation relationship, it can be obtained:

1.The logarithm of the product of two positive numbers is equal to the sum of the logarithms of these two numbers of the same base, i.e.: 2

The logarithm of the quotient of two positive numbers is equal to the difference between the logarithm of the large number of the dividated number minus the logarithm of the dividing number of the same base, i.e.: 3Bottom change formula.

Which question is it?

The second question. lg100-2+1/2＝1/2

log is based on the logarithm of 25 losses of ten, plus the logarithm of log with ten as the base and four laps as the bottom of the game, the answer is the logarithm of log with ten as the base of 100, and the final result is two.

Then the log of the second seven is based on seven, and the exponential answer of the logarithm of two is two.

The last log 19 vd 2 logarithm can be written as log with the square of the vertical cons three as the base of the macro family, and the logarithm of two can finally put forward 1 2, and then log with two as the base and the logarithm of three times the logarithm of the absolute balance log with three as the base two is the conclusion of the bottom change formula is one.

Can the teacher write the complete process by hand.

log: 2 as the bottom of the search for Huai, 3 times the lead calendar, log is based on 3 = log(2)3*log(3)2=lg3 lg2*lg2 lg3=lg3*lg2 (lg2*lg3)=lg3 lg3*lg2 lg2=log(3)3*log(2)2=1*1=1

The first ones are very simple, you know, mainly the last one.

Teacher: Is this an odd or even function.

Non-odd and non-even functions.