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Vikki [24]
3 years ago
13

I need help in this question.

Mathematics
1 answer:
alexgriva [62]3 years ago
4 0

7n-13 is the answer for this


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How does adding the log together automatically mean that it is a factorial?
andreyandreev [35.5K]

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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