How to prove logarithm theorem loga (MN) = loga m + loga n?

How to prove logarithm theorem loga (MN) = loga m + loga n?

Take exponents on both sides of the equation
Left = aloga (MN) = Mn
Right = a [loga (m) + loga (n)] = [loga (m)] * [loga (n)] = Mn
Proof of proposition

If 3 is the logarithm of low 4 * 4 is the logarithm of low 8 * 8 is the logarithm of low M = 4 is the logarithm of low 16, then M is

Taking 3 as the logarithm of low 4 * taking 4 as the logarithm of low 8 * taking 8 as the logarithm of low M = taking 4 as the logarithm of low 16
Using the formula of changing bottom
(lg4/lg3)*(lg8/lg4)*(lgM/lg8)=2
lgM/lg3=2
The results are as follows
log3(M)=2
M=3²=9

Q: logarithm LG is less than ten
lg1=?lg2=?lg3=?lg4=?lg5=?lg6=?lg=?lg8=?lg9=?lg10=1

lg1=0
lg2=0.3010
lg3=0.4771
lg4=0.6021
lg5=0.6990
lg6=0.7782
lg7=0.8451
lg8=0.9031
lg9=0.9542
lg10=1

Let u = {1,2,3,4,5,6,7,8}, a = {x belongs to Z | 0 less than x less than or equal to 6}, B = {4,6}, find anb
Let u = {1,2,3,4,5,6,7,8}, a = {x belongs to Z | 0 less than x less than or equal to 6}, B = {4,6}, find anb?

A = {x belongs to Z | 0 less than x less than or equal to 6} = {1 2 3 4 5 6}
B={4,6}
AnB={4,6}

What are the mistakes in the following English sentences and how to correct them?
1.The reasons of the problems,in my opinions,has three.
2.Because the number of cars was too much.
3.People usually wait in the roads.
4.The number of cars increased slowly.
5.The government need to bulid more roads,

1. Has should be changed to have, because the subject is plural
2. Too much should be changed to too large
3.on the road,in the street
4. If the context is general tense, increased should be increases
5. Need should be needs

Beijing holds the Olympic Games in 2008, which is a leap year. The Olympic Games are held every four years. So is the year of the Olympic Games a leap year? Why

No, the second Paris in 1900 was not a leap year
The Olympic Games should be held every four years. The year of the Olympic Games is usually a leap year
The leap year of the Gregorian calendar is as follows: the earth's revolution around the sun is called a return year, which is 365 days older than the return year by 5:48:46 seconds. Therefore, the Gregorian calendar has an ordinary year and a leap year. The ordinary year has 365 days, which is 0.2422 days shorter than the return year, and a total of 0.9688 days shorter than the four years. Therefore, one day is added every four years, and this year has 366 days, which is a leap year, After 400 years, there will be 3.12 more days, so there will be three less leap years in 400 years, that is, there will be only 97 leap years in 400 years, so the average length of the Gregorian calendar year is similar to the regression year. Therefore, it is stipulated that if the year is a whole hundred, it must be a multiple of 400 to be a leap year. For example, 1900 and 2100 are not leap years
The earth we live on always revolves around the sun. It takes 365 days, 5:48:46, that is 365.2422 days for the earth to revolve around the sun. For convenience, a year is set as 365 days, which is called an ordinary year. In this way, every four years there will be almost one more day. Adding this day to February, the year will have 366 days, which is called a leap year
Usually, every four years there are three ordinary years, a leap year. The Gregorian calendar year is a multiple of 4, generally a leap year
According to the calculation of a leap year every four years, an average of 0.0078 more days will be calculated every year. In this way, after four hundred years, about three more days will be calculated. Therefore, three leap years will be reduced every four hundred years. Therefore, it is stipulated that the Gregorian calendar year is a whole hundred, and it must be a multiple of 400 to be a leap year, not a multiple of 400 or an ordinary year
In other words, the earth we live on always revolves around the sun. It takes 365 days, 5:48:46, that is 365.2422 days for the earth to revolve around the sun. For convenience, a year is set as 365 days, which is called an ordinary year. In this way, almost one more day is needed every four years. If we add this day to February, there will be 366 days in the year, which is called the year
Usually, every four years there are three ordinary years, a leap year. The Gregorian calendar year is a multiple of 4, generally a leap year
According to the calculation of a leap year every four years, an average of 0.0078 more days will be calculated every year. In this way, after four hundred years, about three more days will be calculated. Therefore, three leap years will be reduced every four hundred years. Therefore, it is stipulated that the Gregorian calendar year is a whole hundred, and it must be a multiple of 400 to be a leap year, not a multiple of 400 or an ordinary year
That is what we usually say:
One leap in four years, no leap in a hundred years, and another leap in four hundred years
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What is minus three and a quarter plus two and a third
Hurry!

11 out of 12

Xiaoming has four times as many glass balls as Xiaogang. If Xiaoming gives Xiaogang 10, the ratio of their glass balls is 3:2. How many do they have?

Let there be X
（4x-10）/（x+10）=3/2
x=10

English translation of time (2.30) (3.30) (3.00) (2.15) (1.45) (2.45)

half past two
half past three
three o'clock
a quarter past two
a quarter to two
a quarter to three

When the gardener uses the scissors as shown in the figure to trim the branches, he often puts the branches as close as possible to the scissors axis O. The purpose of doing this is to ()
A. Increase the resistance arm, reduce the distance of power movement B. reduce the power arm, reduce the distance of power movement C. increase the power arm, save effort D. reduce the resistance arm, save effort

If the branch is close to the scissor axis as far as possible, the resistance arm L2 will be reduced, while the power arm L1 and resistance F2 will remain unchanged, ∵ f1l1 = f2l2, ∵ F1 = f2l2l1 will become smaller, that is, labor saving