ChatterBank0 min ago

# For What Value Of X Is X! = Ln(X)?

For what value of x is x! = ln(x)?

from experimentation:

f 5.2903160

_1.39938e_5 less than 0

f 5.2903161

1.03394e_6 more than 0

Where f is function x! - ln(x)

So apart from x=0, there is also a result for x between 5.2903160

and 5.2903161 where f(x') = 0.

Is there a formula to calculate the value of x' exactly?

Does the value x' have any "special significance"?

I assume that after x', there are no further occurrences of x where f(x)=0?

from experimentation:

f 5.2903160

_1.39938e_5 less than 0

f 5.2903161

1.03394e_6 more than 0

Where f is function x! - ln(x)

So apart from x=0, there is also a result for x between 5.2903160

and 5.2903161 where f(x') = 0.

Is there a formula to calculate the value of x' exactly?

Does the value x' have any "special significance"?

I assume that after x', there are no further occurrences of x where f(x)=0?

# Answers

Best Answer

No best answer has yet been selected by RSDonovan. Once a best answer has been selected, it will be shown here.

For more on marking an answer as the "Best Answer", please visit our FAQ.Have you tried plotting the two functions and seeing where they cross. I think they cross only once or twice. I know you say you found 2 but I am not sure what the first one was since ln(0) is undefined

To JD: Logarithms and exponentials are the exact opposites of each other. So log_a (a^x) = x, for all x, where a is the base of the logarithm.

So I'm guessing the answer to your question is "no". But it is the only positive value of x that works.