Using the logarithm of the bottom formula, calculate Log 25 (not 25, the same below) × log 54 = 2? log2 3×log3 4×log4 5×log5 6×log6 7×log7 8=3?

Using the logarithm of the bottom formula, calculate Log 25 (not 25, the same below) × log 54 = 2? log2 3×log3 4×log4 5×log5 6×log6 7×log7 8=3?

log2 5 ×log 5 4 =(lg5/lg2) * (2lg2/lg5)=2
log2 3×log3 4×log4 5×log5 6×log6 7×log7 8
=(lg3/lg2) * (2lg2/lg3)*(lg5/2lg2) * (lg6/lg5)*(lg7/lg6) * (3lg2/lg7)
=2*(3/2)
=3

A problem about the formula of changing base of logarithm
I don't know how he got 2lg5 = 2 (1-lg2)?

2lg5=lg25=lg100/4=lg100-lg4=2lg10-2lg2=2(1-lg2)

8. The results are as follows: (1) every 100 grams of carrot contains 700 micrograms of vitamin A, and the content of carotene is 9 / 10 less than that of vitamin A?
(2) The calcium content of corn is 22 mg / 100g, 9 / 20 less than that of millet?
9. Qingdao municipal government has made a series of investment plans to host the 2008 Olympic sailing competition, including 5 billion yuan for competition venues and 20 billion yuan for environmental protection and greening
(1) The investment in road, bridge and wharf is one-half more than that in environmental protection and greening. How many billion yuan is the investment in road, bridge and wharf?
(2) The investment in competition venues, environmental protection and greening, roads, bridges and wharves accounts for 5 / 7 of the total investment. How many billion yuan is the planned total investment?
All the above are solved by equation and equivalent relation

With carotene x microgram
(1-9 / 10) x = 700
One tenth x = 700
x=70
Let's set the concentration of calcium x mg
(1-9 / 20) x = 22
11 / 20 x = 22
x=40
The total investment is x billion yuan
(X-200) △ 200 = half
x=300
(4) The total investment is x billion yuan
(50+200+300)÷x=5÷7
X = 77 billion yuan
I'm so tired. I can use fraction instead of division. Have you learned it?

X-30 = 1.8x-94 is this. We must say the formula or something

X-30=1.8X-94
94-30=1.8X-X
64=0.8X
X=64/0.8
=80

Decomposition factor: ① 3a3-18a2 + 27a ② x2 + 4xy + 4y2-2x-4y-3

（1）3a3-18a2+27a=3a（a2-6a+9），=3a（a-3）2；（2）x2+4xy+4y2-2x-4y-3，=（x+2y）2-2（x+2y）-3，=（x+2y-3）（x+2y+1）；

Factorization of (A-4) ^ 4 + (a + b) ^ 4 + (a ^ 2-B ^ 2) ^ 2
Answer quickly, hurry

The original formula = (a-b) ^ 4 + 2 (A & # 178; - B & # 178;), # 178; + (a + b) ^ 4 - (A & # 178; - B & # 178;), # 178;
=(a-b)^4+2(a-b)²(a+b)²+(a+b)^4-(a²-b²)²
=[(a-b)²-(a+b)²]²-(a²-b²)²
=(a²-2ab+b²-a²-2ab+b²)²-(a²-b²)²
=(4ab)²-(a²-b²)²
=(2ab+a²-b²)(2ab-a²+b²)

Factorization of (a + b) ^ 2-4 (a + b) (a-b) + 4 (a-b) ^ 2

（a+b）^2-4（a+b）（a-b）+4（a-b）^2
=[(a+b)-2(a-b)]²
=(-a+3b)²;
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Factorization a ^ 2-B ^ 2-4 (a-b)
Speed

a^2-b^2-4(a-b)
=（a+b）（a-b）-4(a-b)
=(a+b-4)(a-b)
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The following formula is factorized by the method of group decomposition: the square of a-b-the square of A-B 4x + the square of 4x-y + 1
It must be solved in the way mentioned above

a^2-b^2-a-b=(a^2-b^2)-(a+b)=(a+b)(a-b)-(a+b)=(a+b)(a-b-1).
1 should be y
(4x)^2 +4x-y ^2+y=(4x+y)(4x-y)+(4x+y)=(4x+y)(4x-y+1).

Use holistic thinking to factorize the following formula!
1、（x+2y)²—2（x+2y)+1
2、（x+y）²—14（x+y）+49
3、（a+b）²—4（a+b-1）

1.=[(x+2y)-1]^2=(x+2y-1)^2
2.=(x+y-7)^2
3.=(a+b)^2-4(a+b)+4=(a+b-2)^2