Oh god, here comes another math post! I can feel it coming on, like werewolfism during the full moon.

I'm only passingly familiar with logarithms, so this, like everything I've stumbled on, has probably already been discovered, but


Is a pretty good approximation (within a couple percentage points, or three or more digits) of the natural logarithm for all the numbers I've checked it on.

For example if

n = 690841693

ln(n) = 20.35342125707679

while our estimate using the above formula comes out to:

n/(1/((n**(1/n))-1)) = 20.353421612948146

Am I missing something obvious here, and if so, what?

Am I doing the idiot savant thing again, or am I just being an idiot again?

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    Math sucks.
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    yes, but I love it.

    I'm the Picasso of math. Fucking terrible at it. I want to be the *van gogh* of math.

    Maybe if I cut off my ear and mail it to my love interest...

    Edit: Is my math bad here or do you mean math in general?
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    Apparently it becomes more accurate the larger the number.

    It is accurate only for the unit digit, up to n=299.

    At n = 446, it becomes accurate to two digits.

    At n = 6975 it is three digits accurate and so on.

    If anyone can find counter examples in these ranges where it is *less* accurate than the rest of the range, that would be cool.
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    @Wisecrack I absolutely hate math lol

    I suck at most of it and it's just not my cup of tea.
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    It's way off for values below 1 (including negative numbers), other than that it's pretty close. But really, exponential function takes exactly as long to compute as its inverse, the logarithmic function - that given, it's faster to just use ln(n).
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    I'm so untrained at math I wasn't aware expotentials were the inverse of logarithms lol.

    I just hate the idea of relying on a magic button.
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    Simply plot the difference of your funktion and ln x:

    On a linear scale (adjust x range at the end) :

    Using a logarithmic x axis :
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    You are a god.

    I will now proceed to trade you gold in exchange for glass beads and wolfram alpha plots.
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    Also Kraator, I'm new to plots. Does it indicate the two converge, or diverge?
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    Hey Kraator, it's probably a lot to ask, and I know I troll and shitpost a bit, in addition to being genuinely ignorant of a lot of things (even I can only tolerate so much self-embarrassment), but would you be willing to explain the difference for me about your two plots and what they mean?
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