We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
57
8
avatar

what is 4 to the power of 2012

 Nov 4, 2019
 #1
avatar
0

4^2012 = 2.2115794807575113474152581518103 x 10^1211

 Nov 4, 2019
 #2
avatar+105972 
0

Can you do it with an ordinary old fashioned calculator?

I can but I am asking guest answerer if he/she can.

Melody  Nov 4, 2019
edited by Melody  Nov 4, 2019
 #3
avatar
0

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
avatar+105972 
0

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
avatar
+1

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
avatar+105972 
+1

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
avatar
+1

Wow! What a beautiful solution!! 

Guest Nov 4, 2019
 #8
avatar+105972 
0

thanks guest, I hope you understand it :)

Melody  Nov 4, 2019

28 Online Users

avatar
avatar
avatar
avatar