1
$\begingroup$

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?

  • 0
    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).2012-02-12
  • 0
    @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.2012-02-12
  • 0
    @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.2012-02-12
  • 2
    @MarcvanLeeuwen: Ahh, so the question would perhaps be better worded as "Since $(1.001)^{1259}\approx3.52$ and $(1.001)^{2062}\approx7.85$, $(1.001)^{3321}\approx ?$"2012-02-12
  • 0
    @Isaac: Most certainly.2012-02-12

2 Answers 2

7

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

  • 2
    Cute, I don't know why haven't I thought of this.2012-02-12
0

$(1.001)^{3321}==(1.001)^{1259+2062}=>(1.001)^{1259}×(1.001)^{2062}$

  • 3
    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.2013-06-09