Math problem where graphing calculator may slow you down...
08-18-2014, 10:28 PM
Post: #12
 Thomas Klemm Senior Member Posts: 1,769 Joined: Dec 2013
RE: Math problem where graphing calculator may slow you down...
(08-14-2014 05:12 PM)Thomas Klemm Wrote:  similarly that $$e^{45} < 10^{20} < e^{225}$$

Here's how you can show this with a 4-banger.
For this we want to calculate $$\log(e)$$ where $$\log$$ is the common logarithm (base 10) while $$\ln$$ shall denote the natural logarithm.
Of course we know that $$\log(e)=\frac{\ln(e)}{\ln(10)}=\frac{1}{\ln(10)}$$.
To calculate $$ln(10)$$ we can use the same trick as before but turn it around and calculate the roots:

10
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
$$\sqrt{x}$$
− 1
× 1024 =

This gives us:
2.305174528

Now instead of $$45\times\log(e)$$ we calculate $$\frac{45}{\ln(10)}$$ and get:
19.52129844

Thus indeed $$e^{45}<10^{20}$$ and analogous for $$10^{20}<e^{225}$$.

Cheers
Thomas
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 Messages In This Thread Math problem where graphing calculator may slow you down... - CR Haeger - 08-14-2014, 02:08 PM RE: Math problem where graphing calculator may slow you down... - Thomas Klemm - 08-14-2014, 04:25 PM RE: Math problem where graphing calculator may slow you down... - CR Haeger - 08-14-2014, 04:36 PM RE: Math problem where graphing calculator may slow you down... - Thomas Klemm - 08-14-2014, 05:12 PM RE: Math problem where graphing calculator may slow you down... - Bunuel66 - 08-17-2014, 10:25 PM RE: Math problem where graphing calculator may slow you down... - CR Haeger - 08-18-2014, 03:10 PM RE: Math problem where graphing calculator may slow you down... - walter b - 08-18-2014, 03:41 PM RE: Math problem where graphing calculator may slow you down... - Thomas Klemm - 08-18-2014, 09:47 PM RE: Math problem where graphing calculator may slow you down... - Bunuel66 - 08-18-2014, 06:59 PM RE: Math problem where graphing calculator may slow you down... - aurelio - 08-18-2014, 09:34 PM RE: Math problem where graphing calculator may slow you down... - Bunuel66 - 08-18-2014, 10:26 PM RE: Math problem where graphing calculator may slow you down... - Thomas Klemm - 08-18-2014 10:28 PM RE: Math problem where graphing calculator may slow you down... - Thomas Klemm - 08-18-2014, 10:52 PM RE: Math problem where graphing calculator may slow you down... - Gilles - 11-15-2014, 12:45 PM

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