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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Compute the largest number

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

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How to find the 2319th digit of 1000!

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n^3 = (n+2)!!

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How Light Travels Without Moving: The Feynman Reality Check

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p² - p +1 = n³

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Is x^x=0 solvable?

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When Math Isn’t Based in Reality

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'Hardest' IMO question of 1988 (#6)

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

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

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Solving a cubic equation using Cardano's formula

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

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WHY MARS IS A DEATH TRAP | NEIL DEGRASSE

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

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The most beautiful formula not enough people understand

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Sum of first n cubes - Mathematical Induction

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