Fifty factorial 2

Number Theory Level 3

Find the integer value of n n such that 2 n 2^n gives the best estimate of 50 ! 50! .

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 214.

Ayush G Rai by Ayush G Rai , 20, India

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2 solutions

Roger Erisman
May 11, 2016

ln(50!) = ln(2^n)

ln(50!) = n * ln (2)

148.4778 = n * 0.6931

214.2228 = n so nearest integer = 214

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Excellent solution..+1

Ayush G Rai - 5 years, 1 month ago

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I also used log to solve it ....but can we solve the problem without a calculator ?

Sabhrant Sachan - 5 years, 1 month ago

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I forgot to give the log values.

Ayush G Rai - 5 years, 1 month ago
Ramiel To-ong
May 11, 2016

nice analysis.

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