Originally Posted by

**zachd77** So I'd solve for x and then use a conversion factor to get the length of the paper? Also, where does the 10^(x-1) come from?

$\displaystyle 10^{x-1} = 9^{9^9} \implies x-1 = 9^9 \log_{10}(9) \approx 369693099$, (rounding down to the nearest whole number).

Add 1 to both sides, and we get

$\displaystyle x=369693100$.

Three digits per centimeter means you will need

$\displaystyle \frac{369693100}{3} = 123231033.\overline{33} \text{ centimeters.}$

Converting from cm to km, the answer is approximately 1232.31 km.