Talk:Approximation to Power of 7 by Power of 10

Neat! I also see that $\pi^{175} \approx 10^{87}$, but your 7 example here really takes the cake! --Robkahn131 (talk) 14:41, 22 May 2020 (EDT)

Interesting! I see that $\log \pi = \sqbrk {0; 2, 87, 4, 1, 1, 1, 4, 52, 2, 1, \dots}$, a lot of $1$'s scattered around this one, and the numbers in it are quite small (the first fifty or so are less than $100$)

$\dfrac {87} {175} = \sqbrk {0; 2, 87}$. Perhaps my hypothesis that the size of the next term determines the accuracy of the approximation is, well, inaccurate.

--RandomUndergrad (talk) 05:23, 23 May 2020 (EDT)

Just noticed something super minor - the link to the seventh power is talking about $a^7$, not $7^a$. --Robkahn131 (talk) 17:37, 23 May 2020 (EDT)

good call --prime mover (talk) 17:58, 23 May 2020 (EDT)