+0  
 
0
646
1
avatar

What is 2012^2012. Please dont write infinity

 May 19, 2015

Best Answer 

 #1
avatar+118723 
+5

 

$$\\y=2012^{2012}\\\\
log y=log(2012^{2012})\\\\
log y=2012log(2012)\\\\$$

 

$${\mathtt{2\,012}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2\,012}}\right) = {\mathtt{6\,646.899\: \!488\: \!484\: \!386\: \!68}}$$

 

 

$$\\log y = 6646.89948848438668\\\\
y=10^{6646.89948848438668}\\\\
y=10^{6646}*10^{0.89948848438668}\\\\
y=10^{0.89948848438668}*10^{6646}\\\\$$

 

$${{\mathtt{10}}}^{\left({\mathtt{0.899\: \!488\: \!484\: \!386\: \!68}}\right)} = {\mathtt{7.933\: \!932\: \!191\: \!378\: \!429\: \!9}}$$

 

so

$$\\2012^{2012}=7.9339321913784299 \times 10^{6646}$$

 

That is an approximations  :)

 

I learned to do this from CPhill.    Thanks Chris  

 May 19, 2015
 #1
avatar+118723 
+5
Best Answer

 

$$\\y=2012^{2012}\\\\
log y=log(2012^{2012})\\\\
log y=2012log(2012)\\\\$$

 

$${\mathtt{2\,012}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2\,012}}\right) = {\mathtt{6\,646.899\: \!488\: \!484\: \!386\: \!68}}$$

 

 

$$\\log y = 6646.89948848438668\\\\
y=10^{6646.89948848438668}\\\\
y=10^{6646}*10^{0.89948848438668}\\\\
y=10^{0.89948848438668}*10^{6646}\\\\$$

 

$${{\mathtt{10}}}^{\left({\mathtt{0.899\: \!488\: \!484\: \!386\: \!68}}\right)} = {\mathtt{7.933\: \!932\: \!191\: \!378\: \!429\: \!9}}$$

 

so

$$\\2012^{2012}=7.9339321913784299 \times 10^{6646}$$

 

That is an approximations  :)

 

I learned to do this from CPhill.    Thanks Chris  

Melody May 19, 2015

1 Online Users

avatar