Log3 (4 √ 27)

Log3 (4 √ 27)

∵4√27=4√（3^3）=（3^3）^1/4=3^（3*1/4）=3^3/4
∴log3(4√27)=log3（3^3/4）=3/4

How to multiply logarithms with different bases?

Generally, it's hard to simplify. Of course, some can be calculated by changing the bottom formula
For example, log (2) 3 × log (3) 4 = log (2) 3 × log (2) 4 / log (2) 3 = log (2) 4 = 2
Log (a) B here is the logarithm with a as the base and B as the true number
Bottom changing formula: log (a) B = log (c) B / log (c) a
In this way, the logarithm based on a is transformed into logarithm based on C

Is there a formula for logarithm operation with the same base?

The formula of operation addition of logarithm with the same base: logab + logac = logabc (a stands for base)
The formula of subtraction of logarithm with the same base: logab - logac = logab △ C (a stands for base)
There are no formulas for multiplication, division, power and root of logarithm with the same base

Suppose you are Li Hua, a ninth grader in a middle school. During the summer vacation, you went to Australia. After the beginning of school, the teacher asked you to give a report to other students,
Focus on the difference of Australian English. About 50 words are required
With Chinese

Australian is a beautiful country, but Australian English is a lot different from American English. It is a non-rhotic language with forty-eight sounds. Twenty of them are vowels and twenty-eight cons...

√(1-√2)^2+√(√2-√3)^2.+√(√99-√100)
√(1-√2)^2+√(√2-√3)^2....+√(√99-√100)^2

√(1-√2)^2+√(√2-√3)^2.+√(√99-√100)^2
＝（√2－1）+（√3－√2）+…… +(√100-√99)
=√100 - 1
=10 - 1 = 9

What is the difference between dot product and cross product of vector? What is the right hand rule

Use "*" to represent the dot multiplication symbol, and (a, b) to represent the angle between vector a and vector B
The point product of a vector is a number
a*b=|a|×|b|×coc(a,b)
The cross product of a vector is a vector whose module is
|a×b|=|a|×|b|×sin(a,b)
Its direction is determined according to the right hand rule: bend the palm of the right hand (the action of praising others), the thumb is outward, the other four fingers bend in the same direction as the corner from a to B, and the direction of the thumb is the direction of a × B

A train departing from a station is moving in a straight line with uniform acceleration on a straight track. It is known that the length of the train is l, the speed of the locomotive passing a road sign is V1, and the speed of the tail passing the road sign is v2. The acceleration a of the train is calculated

It's equivalent to walking l distance, speed from V1 to V2, 2Al = the square of V2 - the square of V1, just take it in

LIM (x2 + X-6) / (x3-8) (x tends to 2)

(x tends to 2) LIM (x2 + X-6) / (x3-8) = Lim [(X-2) (x + 3)] / [(X-2) (x ^ 2 + 2x + 4)] = LIM (x + 3) / (x ^ 2 + 2x + 4) = 5 / 12

Given that the general term formula of sequence {an} is an = (n + 2) (78) n, then when an gets the maximum value, n is equal to______ ．

From an + 1An = 78 (n + 3) n + 2 = 7n + 218n + 16 = 78 (1 + 1n + 2) ≥ 1, the solution is n ≤ 5, and 1n + 2 monotonically decreases. When n = 5 or 6, an gets the maximum. So the answer is: 5 or 6

I hope you will come back soon

i hope you can come back soon