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# what is 4 to the power of 2012

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what is 4 to the power of 2012

Nov 4, 2019

#1
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4^2012 = 2.2115794807575113474152581518103 x 10^1211

Nov 4, 2019
#2
+109518
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Can you do it with an ordinary old fashioned calculator?

Melody  Nov 4, 2019
edited by Melody  Nov 4, 2019
#3
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With Windows 10 comes an HP calculator that can calculate up to 10^10,000 and it has a "mod" key on it as well.

Nov 4, 2019
#4
+109518
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Yes I know there are calculators online that can do it.

I do not think that this is how guest was expected to answer this question.

I asked you if you knew how to do it with a standard old fashioned calculator. (or with the web2.0 calc if you want)

Melody  Nov 4, 2019
#5
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I didn't answer your question properly! You CAN use any ordinary calculator and calculate ANY very large number by using the "Log Key base 10". Example: 25^1E12. You simply take the exponent, or 1E12 and multiplied it by Log 25 base 10. You should get:1,397,940,008,672.037609572522210551. Then you would raise the fractional part to the power of 10 thus. 10^0.037609572522210551 =1.0904595806948112697717659697915 x 10^1,397,940,008,672.

Guest Nov 4, 2019
#6
+109518
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ok

Here is how I would present the answer.

$$y=4^{2012}\\ log_{10} \;y=log_{10} \;4^{2012}\\ log_2 \;y=2012\;log_2 \;4\\ log_2 \;y=2012*2\\ log_2 \;y=4024\\ \frac{log_{10}\;y}{log_{10}\;2}=4024\\ log_{10}\;y=4024*log_{10}2\\ log_{10}\;y\approx 1211.344703\\ y\approx 10^{1211.344703}\\ y\approx 10^{0.344703}*10^{1211}\\ y\approx 2.211581763*10^{1211}\\$$

Melody  Nov 4, 2019
#7
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Wow! What a beautiful solution!!

Guest Nov 4, 2019
#8
+109518
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thanks guest, I hope you understand it :)

Melody  Nov 4, 2019