The question is motivated from the following problem:
At a $15$ percent annual inflation rate, the value of the dollar would decrease by approximately one-half every $5$ years. At this inflation rate, in approximately how many years would the dollar be worth $\frac{1}{1,000,000}$ of its present value?
$A.25\quad B.50\quad C.75\quad D.100\quad E.125$
Finally one may get $10^6=2^n$ and $5n$ is the desired approximation. With a step of calculation, $$n=\frac{6\ln10}{\ln 2}.$$ I have no idea how to go on without a calculator. Are there any tricks/techniques for solving the problem?