What is the meaning of "base truth is the same as logarithm, positive base truth is different from logarithm, negative logarithm" in logarithmic function,

If both the base number and the true number are numbers greater than 1 or numbers between 0 and 1, then their values are positive
If one of the base number and the true number is greater than 1, and the other is a number between 0 and 1, then its value is negative. Take a look at the image of logarithmic function,

What is the definition of the logarithm of 4x-3 with 5 as the base under the function y = root

log5(4x-3)>=0
We get 4x-3 > = 1
x>=1

Practical problems
1. Zhang Ming's family used to use 28 tons of water per month. After using the water-saving faucet, they used to use two more months of water per year. Now how many tons of water per month?
2. There are 1800 pear trees in the orchard, accounting for 3 / 5 of the total number of fruit trees in the orchard, while the number of peach trees is equivalent to 5 / 12 of the total number of fruit trees in the orchard. How many peach trees are there in the orchard?
3. Build a road. When it reaches 4 / 5 of the road, it will be 100 meters away from the end. How long is the road?
4. A and B went to the bookstore to buy books and brought 108 yuan in total. A spent 2 / 4 of his own money and B spent 80% of his own money. The amount of money left by them was exactly the same. How much money did they each bring?
5. Immerse a piece of ore into a round main body shaped water container, the water surface of the container rises from the original 8 cm to 9.2 cm, and the ground diameter of the container is 10 cm. How many cubic centimeters is the volume of the ore?
6. The school library has newly purchased three kinds of books: story books, science fiction books and comic books. Among them, story books account for 25% of the total. The ratio of science fiction books to the other two books is 1:5. There are 140 comic books. How many of the three kinds of books have been purchased?
7. If a commodity is sold at a fixed price, the profit will be 50 yuan per unit. If 10 units are sold at 75% of the fixed price, as much as 12 units are sold at a reduced price of 30 yuan per unit, how much is the price of this commodity?

1. (28 * 12) divided by (12 + 2) = 24 (T) 2, (1800 divided by 3 / 5) multiplied by (5 / 12) = 1250 3, 100 divided by (1-4 / 5) = 500 4, let a and B take X and Y elements respectively, then there is the equation system {x + y = 108. ① (1-2 / 4) x = (1-80%) y.. ②

How many tons of water is a cubic meter of water

One side = 1000 liter = 1000 cubic decimeter = 1000kg = 1T

1/2,-2/5,3/10,-4/17,____ ,-6/37,……

(n + 1) power of (- 1) × n / (n & sup2; + 1)
5/26

1233+1=( )^2;2345+1=( )^2；11121314+1=（）^2;36373839+1=( )^2
Please summarize the rules of the above formula in words
And explain this rule with the knowledge of factorization

Let four multiplicative numbers be n, N + 1, N + 2, N + 3, then n * (n + 1) * (n + 2) * (n + 3) + 1 = (n ^ 2 + 3N + 1) ^ 2. The first one is wrong, which is 1 * 2 * 3 * 4 + 1

How to improve the ability of mathematical calculation
Or will be very careless miscalculation a lot, and then the results and others a lot worse, how to improve

You need to analyze your own situation first, and then apply the right medicine to the case:
Two kinds of bad mentality of one calculation
The main reason is that students despise psychology. They think that the calculation problem is a "dead problem", and they don't need to use their brains to think. They ignore the analysis of the calculation problem and the check after calculation. The second reason is fear psychology. Students think that the calculation problem is boring. Whenever they see many calculation steps or figures, they will be bored, lack of patience and confidence, so the calculation is not accurate
2. Unskilled knowledge and skills
In this part of calculation, there is no complex concept nature. As long as students fully understand and master it firmly, they can form very good calculation skills. However, due to the basic skills such as oral calculation, unclear calculation rules, and lack of basic calculation skills, this is a major problem of calculation errors
Three bad calculation habits
Some students are not willing to write because of their sloppy handwriting; whether they are proficient in numeral or not, they are not willing to do it; some students do not use calculus paper, but do it on the desk or on the back and edge of the test paper at will; after the calculation, they will not use estimation and checking methods to check it carefully

1. It is known that m.n denotes different monomials, and 3x (m-5x) = 6x & sup2; Y & sup3; + n
2、x²+6xy+( )=( )²
3. () & sup2; + 2 / 3 (3 / 2) XY + Y & sup2; = () & sup2;
4、（a+2x)(a-2x)=( )²-（）²=（）
5、（-1/3x-1)(1/3x-1)=( ）²-（）²=( ）
Solve one or two of them, and you'd better answer all of them

2、x²+6xy+(9y²)=(x+3y)²3、（1/9x²）²+2/3xy+y²=（1/3x+y）²4、（a+2x)(a-2x)=(a)²-(2x）²=(a²-4x²）5、（-1/3x-1)(1/3x-1)=(1/3x）²-(1）²=(1/...

5 / 3 * 3 / 5 equals 3 / 1 / 3 / 1 equals 7 / 8 * 87 equals a * what equals 1

1 / a (a number multiplied by the reciprocal of the number equals one)

What is the meaning of "base truth is the same as logarithm, positive base truth is different from logarithm, negative logarithm" in logarithmic function,