6. The least common multiple of 12, 20, 30, 42, 56

6. The least common multiple of 12, 20, 30, 42, 56

Your numbers are exactly 2 * 3, 3 * 4, 4 * 5, 5 * 6, 6 * 7, 7 * 8
So the least common multiple is 5 * 6 * 7 * 4 = 840

Find the value of logarithm of 25 with base 2
I am a beginner, hope to have a template

log2(25)=log2(5^2)=2log2(5)

Given the logarithm of ㏒ 3M = (- 1) / ㏒ with 2 as the base 3, then M =?

log3 m=-1/log 2 3
Log2 M / log2 3 = - 1 / log2 3, [bottom changing formula]
Log2 M = - 1 = - log2 2 = the - 1 power of log2 2
The - 1 power of M = 2 = 1 / 2

To solve the equation: ㏒ logarithm of base 10 (x-178; - 3) -㏒ logarithm of base 10 (3x-5) = 0

㏒ logarithm of base 10 (x-178; - 3) -㏒ logarithm of base 10 (3x-5) = 0
Log ㏒ base 10 (X & ㏒ 178; - 3) / (3x-5) = 0 = ㏒ logarithm of base 10 1
So (X & # 178; - 3) / (3x-5) = 1
x²-3x+2=0
（x-1)(x-2)=0
X = 1 or x = 2
Because the logarithm X & # 178; - 3 is greater than or equal to 1, X is greater than or equal to 2 or X is less than or equal to - 2
And 3x-5 is greater than or equal to 1, X is greater than or equal to 2
So x = 2

On a 1:5000000 map, the distance between a and B is 6cm. On another 1:6000000 map, how many cm is the distance between a and B?

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6 cm △ 1 / 5 000 × 1 / 6 000
=5 cm
The distance between the two places is 5cm
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⊙ ω⊙ find the minimum value of y = (X & # 178; + 5) / √ (X & # 178; + 4) if a > 0, b > 0 and a & # 178; +
Find the minimum value of y = (X & # 178; + 5) / √ (X & # 178; + 4)
If a > 0, b > 0 and a & # 178; + (B & # 178 / 2) = 1, find the maximum value of 1 + B & # 178; under the root of a times

There are six tons of coal in a canteen. If one sixth of the coal is burned every day, how many days can the coal be burned

Method 1 1 divided by 1 / 6 = 6 days method 2 6 divided by (6 * 1 / 6) = 6 divided by 1 = 6 days

A mathematical problem of finding the maximum of inequality
Given the function f (x) = x ^ 2 + ax + 3-A, if x belongs to [- 2,2], f (x) greater than or equal to 2 is constant, the value range of a is obtained

We can use the method of finding the most value. We should classify it like this
f(x)=x²+ax+3-a
Axis of symmetry x = - A / 2
(1) If - A / 24
f(x)min=f(-2)=7-3a≥2 a≤ 5/3
To sum up, there is no intersection, and this situation does not exist
(2) If - 2 ≤ - A / 2

The speed ratio of the express train to the local train is 5:7. The two trains go out at the same time from two places 360 kilometers apart, and travel opposite to each other. When they meet, the express train travels more than the local train by [] kilometers

The express train runs 360 (7 + 5) × 7 / 3 = 70 km per hour
The local train runs 360 (7 + 5) × 5 △ 3 = 50 km / h

Solve the system of inequalities {X of 2 > - 1 ① 2x + 1 ≥ 5 (x-1) ② and write out all its integer solutions
Solve the system of inequalities {x 2} - 1 (1) and write out all its integer solutions
2x+1≥5（x-1）②

1 {X of 2}
2x+1≥5（x-1）②
From (1) to (2)
x > -2
From (2)
2x +1 ≥ 5x -5
6≥ 3x
x≤2
So:
-2