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Number of digits of n!

In this video, I used the definition of logarithm and the factorial for real numbers to obtain the number of digits of any factorial. In particular, I found the number of digits for 1000!. The formula was adjusted to use the mid Reimann sum. I have not tested every number for this formula but It worked for the ones I tested. Please leave a comment in the comment section.

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Bernoulli's Inequality
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Bernoulli's Inequality

Compute the largest number
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Compute the largest number

(n-1)!+1 = n^2
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(n-1)!+1 = n^2

How to find the 2319th digit of 1000!
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How to find the 2319th digit of 1000!

n^3 = (n+2)!!
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n^3 = (n+2)!!

How Light Travels Without Moving: The Feynman Reality Check
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How Light Travels Without Moving: The Feynman Reality Check

p² - p +1 = n³
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p² - p +1 = n³

Is x^x=0 solvable?
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Is x^x=0 solvable?

When Math Isn’t Based in Reality
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When Math Isn’t Based in Reality

'Hardest' IMO question  of 1988 (#6)
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'Hardest' IMO question of 1988 (#6)

Only 2 Primes Have This Property. We Don't Know Why.
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Only 2 Primes Have This Property. We Don't Know Why.

Find all natural numbers such that 2^n + n divides 8^n + n
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Find all natural numbers such that 2^n + n divides 8^n + n

What happens if you just keep squaring?
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What happens if you just keep squaring?

Solving a cubic equation using Cardano's formula
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Solving a cubic equation using Cardano's formula

if x+y=8, find the max of x^y (Lambert W function)
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if x+y=8, find the max of x^y (Lambert W function)

WHY MARS IS A DEATH TRAP | NEIL DEGRASSE
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WHY MARS IS A DEATH TRAP | NEIL DEGRASSE

Why Evolution Split Your Brain In Half – Brain Asymmetry with Jim Al-Khalili
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Why Evolution Split Your Brain In Half – Brain Asymmetry with Jim Al-Khalili

The most beautiful formula not enough people understand
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The most beautiful formula not enough people understand

Sum of first n cubes - Mathematical Induction
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Sum of first n cubes - Mathematical Induction

I finally understood why the universe needs imaginary numbers (My mind is blown!)
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I finally understood why the universe needs imaginary numbers (My mind is blown!)

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