LifeLemons@lemmy.ml to Greentext@sh.itjust.worksEnglish · 5 days agoAnon describes pastimagemessage-square78fedilinkarrow-up11.13K
arrow-up11.13KimageAnon describes pastLifeLemons@lemmy.ml to Greentext@sh.itjust.worksEnglish · 5 days agomessage-square78fedilink
minus-squaremarkovs_gun@lemmy.worldlinkfedilinkarrow-up19·5 days agoIf you want to get real nerdy about it this works because the natural logarithm of 2 is ~0.69 (1+i)^n = 2 n log (1+i) = log 2 n = log 2 / log (1+i) For small numbers, log(1+x) ≈ x n ≈ log 2/i log 2 ≈ 0.69 n ≈ 0.69 / i n ≈ 69/100i Which is pretty close to 70/100i which is the approximation.
minus-squareMeThisGuy@feddit.nllinkfedilinkarrow-up3·5 days agothat is pretty nerdy, but I appreciate the thorough explanation
If you want to get real nerdy about it this works because the natural logarithm of 2 is ~0.69
(1+i)^n = 2
n log (1+i) = log 2
n = log 2 / log (1+i)
For small numbers, log(1+x) ≈ x
n ≈ log 2/i
log 2 ≈ 0.69
n ≈ 0.69 / i
n ≈ 69/100i
Which is pretty close to 70/100i which is the approximation.
that is pretty nerdy, but I appreciate the thorough explanation