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So I found this equation $$ e^{20}=10^{20*.43429\dots} = 10^{8.6858\dots} = 10^9 * 10*(-.3141\dots) $$ on this webpage and I'm really confused as to why it isn't matching up whenever I try it. The first two expressions are equal to each other but the third one doesn't equal either of them. Every time I calculate $10^9 * 10*(-.3141\dots)$ I get $-3414100000$ which is different from the other two expressions which equal $485165195.41$. I'm wondering if this is a mistake and if anyone can explain why this isn't working for me. Thanks.

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On that webpage, the last expression has a typo. Rather than $$ 10\wedge 9 * 10*(-.3141\dots) $$ it should be $$ 10\wedge 9 * 10\color{red}{\wedge}(-.3141\dots) $$ This works out because $10^9 * 10^{-.3141}\approx 485176771.21$, which is about what you say the other ones are equal to.

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  • $\begingroup$ Why are you using the wedge symbol? $\endgroup$ – ericw31415 May 22 '18 at 21:52
  • $\begingroup$ @ericw31415 if you're writing mathematics without special formatting, you can use the wedge or carat to denote exponentation. So x^b is x to the power of b. $\endgroup$ – Mike Pierce May 23 '18 at 0:05
  • $\begingroup$ I'm wondering because $\wedge$ and $\mathrm{^}$ are quite different. $\endgroup$ – ericw31415 May 23 '18 at 0:30

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