\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Here are some approximate values:
$$\ln 2 \approx .7 \ {\rm and}\ \ln 10 \approx 2.3\, .$$ 

\noindent Use these approximations and an indirect argument using only
arithmetic to explain how many decimal digits to expect in the number
$2^{40}$. Are you correct?

\vfil\eject\end