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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.

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Can I get some help we just started this today
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Answer:

-2

Step-by-step explanation:

The slope of a line tells us how y responds to a change in x.  If the slope is 2, it means that for every time x increases by 1, will will go up by 2.

We can calculate slope from a line, or with two given points.  I used points (0,4) and (3,-2).  Slope is the "Rise/Run."

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6 0
2 years ago
This is my hardest one so far. plz help.
SVETLANKA909090 [29]

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7 0
3 years ago
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Nostrana [21]

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3 years ago
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KATRIN_1 [288]

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3 years ago
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GarryVolchara [31]

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3 years ago
Read 2 more answers
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