Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $(1.001)^{1259} = 3.52$ and $(1.001)^{2062} = 7.85$, then $(1.001)^{3321}= ?$

what should be the approach in-order to get a solution without electronic aid?

share|cite|improve this question
If you can't get electronic aid, then you can either use a mechanical computer or do the computation by hand. Another hint: $1259+2062=3321$ (done without electronic aid). And since in fact $1.001^{1259}\neq3.52$ (also checked by mere inspection), you can in actually derive any result you like (ex falso sequitur quodlibet: from a false hypothesis any conclusion can be drawn). – Marc van Leeuwen Feb 12 '12 at 13:51
@MarcvanLeeuwen: How did you arrive at $1.001^{1259}\neq3.52$ by inspection? $1.001^{1259}\approx3.51968$, so $3.52$ isn't far off at all. – Isaac Feb 12 '12 at 19:19
@Isaac: By the binomial formula, $1.001^{1259}$ has a digit $1$ at position $3777$ after the decimal point, while $3.52$ doesn't. So they differ. – Marc van Leeuwen Feb 12 '12 at 20:16
@MarcvanLeeuwen: Ahh, so the question would perhaps be better worded as "Since $(1.001)^{1259}\approx3.52$ and $(1.001)^{2062}\approx7.85$, $(1.001)^{3321}\approx ?$" – Isaac Feb 12 '12 at 20:19
@Isaac: Most certainly. – Marc van Leeuwen Feb 12 '12 at 20:20
up vote 7 down vote accepted

$\begin{eqnarray} 1.001^{3321} &=& 1.001^{1259 + 2062} \\ &=& 1.001^{1259} \times 1.001^{2062}\end{eqnarray}$

share|cite|improve this answer
Cute, I don't know why haven't I thought of this. – Quixotic Feb 12 '12 at 13:57


share|cite|improve this answer
Welcome to Math.Stackexchange and thank you for wanting to participate. However, this question is more than a year old and has an answer already which is very similar to your answer. – mrf Jun 9 '13 at 8:28

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.