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why does 2 to the power of 2015 equal infinity?

 Jan 3, 2016

Best Answer 

 #2
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It is a big number with 607 digits long.

 Jan 3, 2016
 #1
avatar+118608 
+5

It isn't. It is just a huge number.

Too huge for the calculator to deal with. :)

 Jan 3, 2016
 #2
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+5
Best Answer

It is a big number with 607 digits long.

Guest Jan 3, 2016
 #4
avatar+118608 
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I decided to practice my skills and see if I can get an approximation of  \(2^{2015}\)

 

 

\(let \;\;x=2^{2015}\\ log_2x=2015\\ \frac{log_{10}x}{log_{10}2}=2015\\ log_{10}x=2015 \times log_{10}2\\ log_{10}x\approx 606.5754413\qquad\mbox{From the calculator}\\ x\approx 10^{ 606.5754413}\\ x\approx 10^{ 0.5754413}\times10^{ 606}\\ x\approx 3.762194983\times10^{ 606}\\~\\ 2^{2015}\approx 3.762194983\times10^{ 606}\\\)

 

Oh I made it slightly longer than necessary.

I could just have said

 

\(x=2^{2015}\\ logx=log2^{2015}\qquad \mbox{both base 10}\\ logx=2015*log2\\ etc\)

 Jan 3, 2016

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