log1／4（x+3）-log4（x-1）=log1／4（x+9）?

log1／4（x+3）-log4（x-1）=log1／4（x+9）?

log1／4（x+3）-log4（x-1）=log1／4（x+9）
lg（x+3）/ lg1/4 -lg(x-1)/lg4=lg(x+9）/ lg1/4
lg（x+3）/-lg4 -lg(x-1)/lg4=lg(x+9）/-lg4
-lg（x+3） -lg(x-1)=-lg(x+9）
lg（x+3）+lg(x-1)=lg(x+9）
（x+3）(x-1)=(x+9）
x^2-x+3x-3=x+9
x^2+x-12=0
(x-3)(x+4)=0
X = 3, x = - 4
So the solution of the equation is x = 3

The number of solutions of the equation 0.5log2 (2x-x ^ 2) = log2 (A-X) about X is discussed

From the problem, we can see that the domain of definition is (0,2) ∩ (∞, a). From the equation, we can get (2x-x * x) = (A-X) * (A-X). After sorting out, we can get 2x * X-2 (a + 1) x + A * a = 0 ①. Now we discuss the number of roots of equation ① under the domain of definition. When △ > 0, then a > 1 + (root sign) 2 or a

In triangle ABC, if a ^ 2-B ^ 2-C ^ 2 = BC, find the size of ∠ a
In triangle ABC, if a ^ 2-B ^ 2-C ^ 2 = - BC, find the size of ∠ a

Elementary school sixth grade mathematics Life Essay
Mathematics story

There are many interesting things in the world of mathematics. For example, in my exercise book of Book 9, there is a thinking question that says: "a bus is driving from the east city to the West City, traveling 45 kilometers per hour, stopping after 2.5 hours, just 18 kilometers from the midpoint of the East and West cities, East

Divide the wire of length 1 into two sections to form a square and a circle. In order to minimize the sum of the areas of the square and the circle, what is the perimeter of the square?

Let the circumference of a circle be x, then the circumference of a square be (1-x) s = π (x / 2 π) ^ 2 + [(1-x) / 4] ^ 2 = x ^ 2 / 4 π + (x-1) ^ 2 / 16 = [(16 + 4 π) / 64 π] [(x ^ 2-8 π X / (16 + 4 π) + 4 π / (16 + 4 π)] = [(16 + 4 π) / 64 π] [(x-4 π / (16 + 4 π)] ^ 2 + 1 / 16 - π / (64 + 16 π) = [(16 + 4 π) / 64 π]]

Given that a = - y * y + AY-1. B = 2Y * y + 3ay-2y-1, and the value of polynomial 2A + B has nothing to do with the value of the letter Y, we can find the value of A

Because a = - y * y + AY-1. B = 2Y * y + 3ay-2y-1,
So 2A + B = 2 (- y * y + AY-1) + 2Y * y + 3ay-2y-1
=5ay-2y-3
=y(5a-2)-3
Let the value of the polynomial 2A + B be independent of the value of the letter y
5a-2 must be equal to 0
So a = 2 / 5 = 0.4

A shop sells some goods. According to the sales situation, the quantity of goods purchased is 50000 pieces, and the goods are purchased in equal quantity in several times (set X pieces for each purchase). The freight for each purchase is 50 yuan, and the goods are purchased immediately after the completion of the sales. Now the average annual (x / 2 pieces) is stored in the warehouse, and the storage fee is 20 yuan per piece. In order to save the freight and inventory fee for a year, how much should the quantity of goods purchased be x?

Suppose that the freight and inventory cost of a year is y yuan, y = 50000 × 50 + x2 × 20 = 25 × 105x + 10x ≥ 225 × 106 = 10000 (10 points) that is, when x = 500, Ymin = 10000 (12 points)

Application: a square, its side length increases by 5 decimeters, the area increases by 125 square decimeters, find the area of the original square
It must be solved by arithmetic!

Side length of original square: (125-5 × 5) / (2 × 5) = 10 (decimeter)
(if you draw a diagram to help understand the above calculation, you can easily understand it!)
Original square area: 10 × 10 = 100 (square decimeter)

It is known that it takes 8 minutes and 20 seconds for the sun to reach the earth, and the gravitational constant is 6.67 times 10 (- 11) power to calculate the mass of the sun

Let the mass of the sun and the earth be m and m respectively, the speed of light be C = 3 * 10 ^ 8 (M / s), the distance between the sun and the earth be r, the time of light from the sun to the earth be t = 500 (s), the time of the earth circling the sun be t (that is, one year), the angular velocity of the earth be w, the constant of universal gravitation be g = 6.67 * 10 ^ 11 [Si], the gravitation of the sun to the earth be f, and the earth circling around the sun be f

The concept of principal stress and normal stress?

Definition: the normal stress on the section with zero shear stress at any point in the body
Stress: the distribution of internal force on the section of a member is called stress. Stress is the internal force concentration at a point on a section of a member under stress. (excerpted from Sun Xun Fang, fourth edition of mechanics of materials 1 above). The stress component perpendicular to the section is called normal stress (or normal stress, expressed by σ); the stress component tangent to the section is called shear stress or shear stress, expressed by τ