1

I just don't know where to start any help is appreciated.

Rayyan Merchant
  • 109
  • 1
    What do you get when you divide the numbers? –  Dec 24 '15 at 07:22
  • Is the answer nine – Rayyan Merchant Dec 24 '15 at 07:23
  • No. ${}{}{}{}{}$ –  Dec 24 '15 at 07:23
  • Can you please tell me the answer – Rayyan Merchant Dec 24 '15 at 07:24
  • How did you get 9 when you divided the numbers? –  Dec 24 '15 at 07:25
  • 2
    Just do what the guy said, do $\frac{3^{20}+3^{22}}{3^{20}}$. – mopy Dec 24 '15 at 07:25
  • The answer is 10 OK got it – Rayyan Merchant Dec 24 '15 at 07:27
  • 2
    Why is this question being downvoted? The user obviously has little choice when he has NO CLUE how to proceed about the question? The user would post about his attempts and where he is stuck in the details of the question ONLY IF he had found a way to proceed. What do the downvoters expect or suggest the user to do? Downvoting the downvotes.... – Deepak Gupta Dec 24 '15 at 07:31
  • @Deepak Gupta Thank you – Rayyan Merchant Dec 24 '15 at 07:34
  • @DeepakGupta The asker here has a lengthy history of posting unmotivated questions that end in phrases along the lines of "I don't know where to start." For what it's worth, I only downvoted after the comment asking for the answer, rather than engaging with (what I hoped to be) an educational line of comments. –  Dec 24 '15 at 07:47
  • @DeepakGupta "I don't know where to start" is NEVER an excuse. Do they know what a number is? If so, that's a start. Do they not know what a number is? Then figuring out what a number is is a start. There is ALWAYS a start, ALWAYS. This is just lazy problem (most likely homework) dumping and I don't want this kind of garbage on math.SE –  Dec 24 '15 at 08:04
  • Oh.. Got it.. Would be nice if down voters explained through a comment why the question is worth down voting.. It will help the user to be more responsible in the future – Deepak Gupta Dec 24 '15 at 08:07

2 Answers2

3

Hint. Factor $3^{20}+3^{22}$ as $3^{20}(1+3^2)$.

Brian Tung
  • 34,160
0

This question is tricky in the wordings. Consider $$\frac{3^{20}+3^{22}}{3^{20}} = \frac{3^{20}(1+3^2)}{3^{20}} = 1+3^2 = 10$$ Hence, $3^{20}+3^{22}$ is 10 times of $3^{20}$. So, $3^{20}+3^{22}$ is $\mathbf {greater}$ than $3^{20}$ by $$10-1=9\; \text{times}$$

Hirofumi Ryo
  • 676
  • 1
    This is incorrect. The usual meaning of $x$ is greater than $y$ by $n$ times is $x = ny$. – Deepak Dec 24 '15 at 07:58
  • Consider the equation of percentage increase: $$\frac{x-y}{y}\times 100% =(\frac xy - 1) \times 100% = (n-1)\times 100% $$ Hence, $x$ is greater than $y$ by $(n-1)$ times if $x=ny$. – Hirofumi Ryo Dec 24 '15 at 08:07
  • It's not that I don't get your point. I am telling you how the phrases "times greater than" and "times less than" are applied in common parlance, which is applicable to this question. In this context, your interpretation is wrong. Lay language is often imprecise. – Deepak Dec 24 '15 at 08:15