This problem has been baffling me for days!

Ink70 · New Member Offline Joined: 08 Nov 2009 Posts: 2

Okay, I'm new here, so I may be wrong, but I believe my question belongs in this section.

If 100% is 10^10, 50% is 10^(10/3), 25% is 10^(10/27), 12.5% is 10^(10/81) and so forth, what is 18.75%? I've noticed that each time the percentage is cut in half, the power factor is reduced by three. But, I have no idea how to get the values in between the numbers. If you know an equation that works for this, please help!

**Posted:** Sun Nov 08, 2009 1:46 pm

pascal12 · Riemann Hypothesis Offline Joined: 18 Mar 2009 Posts: 253

I have no idea what you mean by $100\% = 10^{10}$ and so forth. However, $18.75 = 12.5 + 6.25 = 3\cdot6.25$ . I have no idea what to do from here because the percentages are totally confusing me.

**Posted:** Sun Nov 08, 2009 7:45 pm

AndrewTom

I'm not sure what you mean but there seems to be a $10^{\frac{10}{9}}$ missing. If so, your pattern then suggests that $12.5 + 6.25$ gives $10^{\frac{10}{81}} + 10^{\frac{10}{243}}$ .

**Posted:** Mon Nov 09, 2009 7:28 am

JBL

This problem is extremely poorly posed, and the reconstruction the other posters have gone for doesn't make any sense. (If we were meant to get 18.75 as 12.5 + 6.25, then we should surely also get 12.5 as 6.25 + 6.25, but this doesn't match the proposed pattern (correcting it for the omission that AndrewTom noted by replacing 10/27 and 10/81 with 10/9 and 10/27, respectively).) The most plausible associated problem is the following:

Suppose that $f \colon \textbf{R}_{> 0} \to \textbf{R}$ satisfies $f(x^{1/3}) = \frac {f(x)}{2}$ for all $x$ and $f(10^{10}) = a$ . Find $f(x)$ .

Unfortunately, this problem is also underdetermined: we'll need some additional property like continuity at some point in order to make the proper conclusion for $x > 1$ (or $x \geq 1$ , or whatever). On the other hand, it's not incredibly hard to come up with the unique function continuous on $\textbf{R}_{\geq 1}$ that satisfies this condition.

**Posted:** Mon Nov 09, 2009 12:29 pm

_________________
Joel
Hi Deeps! <3

Ink70 · New Member Offline Joined: 08 Nov 2009 Posts: 2

I'm sorry guys, there was something missing. I had to re-read the problem to see if I missed something, and I did. But, it is still just as confusing.

100% of a number is 10^10, 50% of a number is 10^(10/3), 25% of a number is 10^(10/9), 12.5% is 10^(10/27), 6.25% of a number is 10^(10/81). What is 18.75% of a number?

Thanks for all of your time!

**Posted:** Thu Nov 12, 2009 9:51 am

Poincare

**Posted:** Thu Nov 12, 2009 6:15 pm

_________________
Please visit this website: freerice.com and play for just 5 minutes and help end hunger.

pascal12 · Riemann Hypothesis Offline Joined: 18 Mar 2009 Posts: 253

I'm pretty sure this problem has somehow redefined the definition of percentages.

Every time you multiply the percentage by 2, you multiply the exponent by 3. So if you multiply the percentage by 3, then you multiply the exponent by 4.5, or 9/2? Therefore, that would make $18.75 = 3\cdot6.25 = 10^{\frac {10}{81}\cdot\frac{9}{2}} = 10^{\frac {5}{9}}$ .

**Posted:** Thu Nov 12, 2009 6:22 pm

brainomega

When you multiply the percentage by $x$ , you multiply the exponent by $x\log_23$ . $18.75=6.25\cdot3$ $10^{\frac{10}{81}3\log_23}\approx\boxed{3.86}$

**Posted:** Thu Nov 12, 2009 7:49 pm