4
Wisecrack
76d

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

n/(1/((n^(1/n))-1))

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?

Comments
  • 2
    Math sucks.
  • 1
    @Stuxnet

    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?
  • 0
    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.
  • 1
    @Wisecrack I absolutely hate math lol

    I suck at most of it and it's just not my cup of tea.
  • 1
    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).
  • 0
    @hitko

    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.
  • 1
    Simply plot the difference of your funktion and ln x:

    On a linear scale (adjust x range at the end) :
    https://wolframalpha.com/input/...

    Using a logarithmic x axis :
    https://wolframalpha.com/input/...
  • 0
    @kraator

    You are a god.

    I will now proceed to trade you gold in exchange for glass beads and wolfram alpha plots.
  • 0
    @kraator

    Also Kraator, I'm new to plots. Does it indicate the two converge, or diverge?
  • 0
    @kraator

    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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