1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kari74 [83]
2 years ago
7

How does adding the log together automatically mean that it is a factorial?

Mathematics
1 answer:
andreyandreev [35.5K]2 years ago
6 0

Answer: The answer is given below.

Step-by-step explanation:  We are given an equality involving logarithm and we are to show the implication of L.H.S. to R.H.S.

We will be using the following two properties of logarithm:

(i)~\log_ba=\dfrac{1}{\log_ab},\\\\\\(ii)~log_ab+\log_ac=\log_a(bc).

The proof is as follows:

L.H.S.\\\\\\=\dfrac{1}{\log_2N}+\dfrac{1}{\log_3N}+\dfrac{1}{\log_4N}+\cdots+\dfrac{1}{\log_{100}N}\\\\\\=\log_N2+\logN3+\log_N4+\cdots+\log_N100\\\\=\log_N\{2.3.4...100\}\\\\=\log_N\{1.2.3.4...100\}\\\\=\log_N{100!}\\\\=\dfrac{1}{\log_{100!}N}\\\\=R.H.S.

Hence proved.

You might be interested in
Even number less than 12​
OleMash [197]

Answer:

2,4,6,8,10

Step-by-step explanation:

they are even numbers

5 0
3 years ago
Read 2 more answers
10x - 5=6x-25 idkk help mee
Sunny_sXe [5.5K]

Answer:

10x - 5=6x-25

Step-by-step explanation:

learn it yourself you stupid

4 0
3 years ago
At a basketball game, a vender sold a combined total of 101 sodas and hot dogs. The number of sodas sold was 37 more than the nu
aliina [53]

Answer:

101 - 37 = 64

I hope this is correct

4 0
2 years ago
Reduce 18/32 to lowest terms
Karo-lina-s [1.5K]
18/32 to its lowest terms is 9/16

4 0
3 years ago
Read 2 more answers
Which of the following is the inverse of the function given below?
Mademuasel [1]
Rearrange so x  is the subject:-

(im assuning  the f unction f(x)  = (x + 2) / 7):-


f(x) = (x + 2)/7

7f(x)  = x + 2

x = 7f(x) - 2

replace f(x) by  x and x by another function 

f = 7x - 2


Its D
6 0
2 years ago
Read 2 more answers
Other questions:
  • Dominique wants to use the distributive property to find the value of 15·37+15·63 mentally. Which expression can she use?
    8·2 answers
  • Can u help me with this problem thx
    15·1 answer
  • Can someone help please?? <br><br> I’lginsu edthvukcstghk
    6·1 answer
  • 25 + 47 is the same as<br>+ 50​
    10·1 answer
  • Please help!!! :)))
    5·1 answer
  • Adrianna is attempting to write an inequality from a graph. She knows that the dash boundary line passes through the points (27,
    5·1 answer
  • The product of two factors is 5,600 One factor is 80 What is the other factor?
    8·2 answers
  • (6Q) Find the domain and range.
    6·1 answer
  • Check all that apply
    15·2 answers
  • Please Help!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!