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Hey Everyone I Want answer for this question. Its a very long process spo i am unable to calculate on any calculator or in any program

i want answer for 9^(9^9)

Dont mis understand it as 9^81. it is 9 power of 9 power of 9

I.e 9^9=387420489 so it is 9^387420489 means 9 Power of 387420489

Please reply soon...

DIPAKDHAMNANI  Aug 12, 2015

Best Answer 

 #1
avatar+93677 
+10

9^(9^9) = 9^387420489 

 

let

 

$$\\y=9^{387420489} \\\\
logy=log9^{387420489}\\\\
logy=387420489log9\\\\$$

 

$${\mathtt{387\,420\,489}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{9}}\right) = {\mathtt{369\,693\,099.631\: \!570\: \!368\: \!587\: \!876\: \!1}}$$

 

$$\\logy=369693099.6315703685878761\\\\
10^{logy}=10^{369693099.6315703685878761}\\\\
y=10^{369693099}*10^{0.6315703685878761}\\\\
y=10^{0.6315703685878761}*10^{369693099}\\\\$$

 

$${{\mathtt{10}}}^{{\mathtt{0.631\: \!570\: \!368\: \!587\: \!876\: \!1}}} = {\mathtt{4.281\: \!247\: \!828\: \!802\: \!288\: \!2}}$$

 

$$9^{({9^9})}\approx 4.2812478288022882\times 10^{36969399}$$

Melody  Aug 12, 2015
 #1
avatar+93677 
+10
Best Answer

9^(9^9) = 9^387420489 

 

let

 

$$\\y=9^{387420489} \\\\
logy=log9^{387420489}\\\\
logy=387420489log9\\\\$$

 

$${\mathtt{387\,420\,489}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{9}}\right) = {\mathtt{369\,693\,099.631\: \!570\: \!368\: \!587\: \!876\: \!1}}$$

 

$$\\logy=369693099.6315703685878761\\\\
10^{logy}=10^{369693099.6315703685878761}\\\\
y=10^{369693099}*10^{0.6315703685878761}\\\\
y=10^{0.6315703685878761}*10^{369693099}\\\\$$

 

$${{\mathtt{10}}}^{{\mathtt{0.631\: \!570\: \!368\: \!587\: \!876\: \!1}}} = {\mathtt{4.281\: \!247\: \!828\: \!802\: \!288\: \!2}}$$

 

$$9^{({9^9})}\approx 4.2812478288022882\times 10^{36969399}$$

Melody  Aug 12, 2015

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