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3 years ago

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.

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What is the domain of the function represented in the graph?

alisha [4.7K]

Answer:

0-t-14

Step-by-step explanation:

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5 0

3 years ago

Solve the equation above

saveliy_v [14]

Answer:

X = -2

Step-by-step explanation:

1/2 X (5X-8) = -9

multiply both sides of the equation by 2

2 X 1/2 X (5X - 8) = 2 X (-9)

1 X (5X - 8) = 2 X (-9)

Reduce the numbers with the greatest common divisor 2

5 x -8 = 2 x (-9)

5 x -8 = -18

Move constant to the right by adding its opposite to both sides

5X -8 + 8=-18 + 8

Then eliminate the opposites

5X = -18 + 8

Calculate the sum

5X = -10

Divide both sides of the equation by 5

5X DIVIDE 5 = -10 DIVIDE BY 5

X = -10 DIVIDE BY 5

X = -2

5 0

3 years ago

The diagram shows four graphs match the graphs to the equations

cluponka [151]

Answer:

y=x^2 is graph D

y=1/x is graph A

otherwise, you're right

7 0

3 years ago

Consider the square root function f(x) = sqrt x + 2 + 1 to complete the table of values below. find each missing value and then

Scrat [10]

Given the function :

$f(x)=\sqrt[]{x+2}+1$

We need to find each missing value

Given x = -3 , -2 , -1 , 2 , 7

So, substitute with each value of x to find the corresponding value of f(x)

$x=-3\rightarrow f(x)=\sqrt[]{-3+2}+1=\sqrt[]{-1}+1$

So, there is no value for f(x) at x = -3 (the function undefined because the square root of -1)

$\begin{gathered} x=-2\rightarrow f(x)=\sqrt[]{-2+2}+1=\sqrt[]{0}+1=0+1=1 \\ \\ x=-1\rightarrow f(x)=\sqrt[]{-1+2}+1=\sqrt[]{1}+1=1+1=2 \\ \\ x=2\rightarrow f(x)=\sqrt[]{2+2}+1=\sqrt[]{4}+1=2+1=3 \\ \\ x=7\rightarrow f(x)=\sqrt[]{7+2}+1=\sqrt[]{9}+1=3+1=4 \end{gathered}$

the graph of the function and the points will be as shown in the following image :

5 0

1 year ago

If you know how to do this pls help thankyou!

dmitriy555 [2]

Answer : 49

I hope you understand sorry for the ugly writing

4 0

3 years ago