It is known that LG2, LG (2 ^ x-1), LG (2 ^ x + 3) form an arithmetic sequence to find X

It is known that LG2, LG (2 ^ x-1), LG (2 ^ x + 3) form an arithmetic sequence to find X

2lg(2^x-1)=lg2+lg(2^x+3)
lg(2^x-1)²=lg2(2^x+3)
So (2 ^ x-1) & # = 2 (2 ^ x + 3)
Let a = 2 ^ X
Then (A-1) ² = 2 (a + 3)
a²-4a-5=0
(a-5)(a+1)=0
a=2^x>0
2^x=5
x=log2(5)

If LG2, LG (2x-1), LG (2x-3) are in arithmetic sequence, then x =?

2lg(2x-1)=lg2+lg(2x-3)
Namely
(2x-1)²=2(2x-3)
Just solve it, and pay attention to the value range of X

The original price of a commodity sold in the supermarket is a yuan. There are three price adjustment schemes in the county. First, increase the price by 20%, and then reduce the price by 20%
2、 The price is reduced by 20% now and 20% later
3、 Raise the price by 15% first and lower it by 15%
Are the results of the three price adjustment schemes the same

1、
a(1+20%)(1-20%)=0.96a
2、
a(1-20%)(1+20%)=0.96a
3、
a(1+15%)(1-15%)=0.9775a
So 1 is the same as 2
The original price has not been restored

Let the domain of function y = f (x) be interval [a, b], and G (x) = f (x + 1), then the domain of function g (x) is interval?
What is the relationship between y = f (x) and f (x + 1)?

The answer is wrong
The domain should be (A-1, B-1)
Let t = x + 1, then G (x) = f (T), f (x) definition field is [a, b], then t belongs to [a, b], then x + 1 belongs to [a, b], so x belongs to (A-1, B-1), definition field (A-1, B-1)
The relation is a composite function, and the independent variable X of F (x) is composed to get g (x)
From the perspective of image analysis is the image along the x-axis after translation, you can draw a simple figure, such as y = x and y = x + 1
In physical simple harmonic motion (sinusoidal image), it is a kind of phase transformation. Without considering the complex graphic transformation such as axial reversal, the image transformation learned in senior high school can be seen as the combination of period transformation, amplitude transformation and phase transformation
It is suggested to check the sine cosine function image transformation in high school mathematics trigonometric function, the translation in vector, and the simple harmonic motion in high school physics

It's a quadratic equation of one variable
It is known that the purchase price of air conditioners is 2500 yuan, and shopping malls can sell 8 units per day at 3500 yuan. Now, through investigation, shopping malls can sell 2 more units per day for every 100 yuan decrease. Ask how much the price is, the profit of shopping malls can be increased by 12.5%

Set the price as X Yuan
X-2500 unit profit now
8 + (3500-x) × 2 △ 100 pieces sold now
(x-2500)[8+(3500-x)×2÷100]=(3500-2500)×8×(1+12.5％)
Solve the equation and get x = 3000 or 3400
Try to sell as few goods as possible to get more profit
So the price is 3400 yuan

If a commodity is sold at a reduced price due to seasonal changes, it will still make a profit of 120 yuan if the current price is reduced by 10%. If the price is reduced by 20%, it will lose 240 yuan. How much is the purchase price

Suppose: the current price of this commodity is X
X*(1-10%)-120=X*(1-20%)+240
Solution equation: x = 3120
A: the purchase price of this commodity is 3120 yuan

If n satisfies the quadratic power of (n-2002) + the quadratic power of (2003-n) is equal to 1, find the value of (2003-n) (n-2002)

Because (n-2002) ^ 2 + (2003-n) ^ 2 = 1
So (n-2002) ^ 2 = 1 - (2003-n) ^ 2
Using a ^ 2-B ^ 2 = (a + b) (a-b)
So there are:
(n-2002)^2=[1+（2003-n）]*[1-（2003-n）]；
Simplification: (n-2002) ^ 2 = (2004-n) * (n-2002)
In this case, we need to consider whether the fraction (n-2002) is zero;
If n-2002 = 0, then n = 2002; the original formula holds, so (2003-n) (n-2002) = 0;
If n-2002 ≠ 0, then both sides of the equation are divided by the fraction n-2002 at the same time
There are: n-2002 = 2004-n
Then n = 2003, so 0

When Wang Ming calculated the difference of a polynomial minus 2B ^ 2 + B-5, he forgot to enclose the two polynomials in brackets, so the subtraction formula was invalid
There is no sign change in the last two terms, and the difference between the results is B ^ 2 + 3b-1. According to this, can you work out the polynomial? Can you work out the correct result?
Another question: can 2B multiply 2B simplify?

The difference between value and use value

Something of value must be of use`
What is valuable in use is not necessarily valuable`
For example, sunlight has use value, but it has no value`

The sum of three digit numbers is 16, and ten digit numbers are the sum of one digit number and one hundred digit number. The sum of one hundred digit number and one digit number is 594 larger than the original

The sum of each digit is 16. Ten digit is the sum of one digit and 100 digit. We can get the following result: "ten digit" is 16 △ 2 = 8. If 100 digit is x, then the single digit is (8-x). The equation is: 100x + 8 * 10 + (8-x) = 100 (8-x) + 10 * 8 + X + 594. The simplification is: 99x = 99 (8-x) + 594 (about 11 on both sides): 9x =