Divide a number by what value to reach 1 in a specified number of steps

Question

I would like to divide my number 13255956 by another number over and over again to reach 1 in exactly 255 steps. Through trial and error I managed to find that the number is approximately 1.06.

How might I go about caculating this number precisely?

Sorry if an answer to this aready exists but I wasn't sure of the correct search terms and haven't had luck with my searches.

score 5 · Accepted Answer · answered Sep 19 '21 at 13:26

5

So, you want to solve $$n^{255}=13255956$$

Taking logs, we get $$255\times \ln(n)=\ln (13255956)\implies \ln(n)=.064313\cdots\implies $$ $$ n=e^{.064314\cdots}=1.0664\cdots$$

answered Sep 19 '21 at 13:26

lulu

70,402

8

That's a convoluted way to calculate $n=\sqrt[255]{13255965}\quad$ ;) – Sep 19 '21 at 13:35
Thanks lulu and saucy. – Joe Hamilton Sep 19 '21 at 13:59

Divide a number by what value to reach 1 in a specified number of steps

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