how to solve:- 92!/x!=10^110?

Question

the question is a maths question and ^ means exponential 110 power of ten.

we have 92 naturally occuring elements and 10^100
stars the x in question gives total number of elements that must be present in an cell. Conversely we know x then we can find total number of stars which can have life this concept arises when i want to modify some space theories and this concept leads to a fact that even hydrogen can be main element and constitute celll as we have carbon so does all 92 elements.

Answer 1

x! = 92! /10^110

which is approximately

1.2438414055 * 10^32

The closest value to this is

30! = 2.6525285981 * 10^32

So if x = 30, then x! is approximately 92! /10^110

You cannot get an exact value,
because x must be an integer.

Answer 2

There are no solutions.

Dividing 92!/x! yields 92 * 91 * 90 * .... etc. up to some point. However, 92 is divisible by 23, so the final product is also divisible by 23... but 10^110 is not divisible by 23 so the equality cannot function.

Answer 3

I'll throw in my 2 cents.

Raj solved for x!:

x! = 92!/10^110

The problem, however, is that there is no inverse factorial function, so you can't isolate x by taking the inverse factorial of both sides.

Furthermore, factorial is only defined for integers, and the number on the right is clearly not an integer.

I understand there's a continuous version of the factorial. I think it's called the gamma function? But I don't know much about it.

In any case, you can't really get an answer.

Answer 4

92!=x!*10^110
x!=92!/10^110