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]
3 years ago
7

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

Mathematics
1 answer:
andreyandreev [35.5K]3 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
Solve the following system of inequalities graphically on the set of axes below. State
tankabanditka [31]

Answer:

The answer is definitely C

Step-by-step explanation:

Following the system of inequalities will graph this solution best on the graph, it is the inequality represented in the graph.

ur wlcm :)

correct me if im wrong

brainliest please?

6 0
2 years ago
Find the difference quotient of the exponential function, f(x) = e^x
Orlov [11]

Answer:

Step-by-step explanation:

The difference quotient in general looks like

\frac{f(x+h)-f(x)}{h}   Sometimes the symbol "delta x"  \Delta x   is used instead of h.

For the exponential function, the difference quotient is

\frac{e^{x+h}-e^x}{h}

5 0
3 years ago
In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?
Mrac [35]

Answer:

Cosec <F = 73/55

Step-by-step explanation:

In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?

First you must know that;

Cosecant <F = 1/sin<F

Given

∠G=90°, GF = 48, EG = 55, and FE = 73.

ED ,= hyp = 73

EG = opp = 55*side facing <F

Using DOH CAH TOA

Sin theta = opp/hyp

Sin <F= 55/73

Reciprocate both sides

1/sinF = 73/55

Cosec <F = 73/55

3 0
3 years ago
Which of the following regarding the power of a significance test is/are correct? Select all that apply.As the effect size incre
Tanya [424]

According to the theory on the <em>effect size</em> the following statements are correct:

<em>As the standard deviation increases, the power of the test increases</em>. An increment of the standard deviation means that a larger sample size is required for the test and a larger sample size implies that the power increases, which means that as the standard deviation increases the power also increases.

<em>As the sample size increases, the power of a test increases</em>. When the sample size increases the amount of information increases, this means that the probability of rejecting H0 given that H0 is false increases. In other words, the probability that the significance test performs according to reality is larger.

3 0
3 years ago
What is the slope of a line that passes through the points (3, 1) and (2, 5) Please help! thanks!
Romashka-Z-Leto [24]
3=x1. 1=y1
2=x2. 5=y2

the formula to find slope is y2-y1 divided by x2-x1

so it would be 5-1 over 2-3 which would be 4/-2 and if you need it simplified it would be -2
4 0
3 years ago
Other questions:
  • The family size bottle of sunscreen holds 12 fluid ounces (fl oz) of sunscreen. The regular bottle holds 75% less.How many fewer
    15·1 answer
  • -(-2) and -/-2/ simplify to different numbers
    9·1 answer
  • QUICK!!!!!!!! PLSSS I NEED HELP!!!
    13·2 answers
  • Is 2,925 more than 2,9250
    15·1 answer
  • Can someone help me with this ( also pls tell me if u can't see the picture because I've posted this question many times and it
    8·1 answer
  • What is the solution to the following equation?
    15·1 answer
  • A. Find m<br> b. you write the measures of
    15·1 answer
  • What are ascending number's​
    6·2 answers
  • A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. A regular pentag
    12·2 answers
  • If 8 is added to a certain number, the result is 34. Write an equation to describe this situation.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!