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...
9^(9^9) = 9^387420489
let
$$\\y=9^{387420489} \\\\
logy=log9^{387420489}\\\\
logy=387420489log9\\\\$$
$${\mathtt{387\,420\,489}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{9}}\right) = {\mathtt{369\,693\,099.631\: \!570\: \!368\: \!587\: \!876\: \!1}}$$
$$\\logy=369693099.6315703685878761\\\\
10^{logy}=10^{369693099.6315703685878761}\\\\
y=10^{369693099}*10^{0.6315703685878761}\\\\
y=10^{0.6315703685878761}*10^{369693099}\\\\$$
$${{\mathtt{10}}}^{{\mathtt{0.631\: \!570\: \!368\: \!587\: \!876\: \!1}}} = {\mathtt{4.281\: \!247\: \!828\: \!802\: \!288\: \!2}}$$
$$9^{({9^9})}\approx 4.2812478288022882\times 10^{36969399}$$
9^(9^9) = 9^387420489
let
$$\\y=9^{387420489} \\\\
logy=log9^{387420489}\\\\
logy=387420489log9\\\\$$
$${\mathtt{387\,420\,489}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{9}}\right) = {\mathtt{369\,693\,099.631\: \!570\: \!368\: \!587\: \!876\: \!1}}$$
$$\\logy=369693099.6315703685878761\\\\
10^{logy}=10^{369693099.6315703685878761}\\\\
y=10^{369693099}*10^{0.6315703685878761}\\\\
y=10^{0.6315703685878761}*10^{369693099}\\\\$$
$${{\mathtt{10}}}^{{\mathtt{0.631\: \!570\: \!368\: \!587\: \!876\: \!1}}} = {\mathtt{4.281\: \!247\: \!828\: \!802\: \!288\: \!2}}$$
$$9^{({9^9})}\approx 4.2812478288022882\times 10^{36969399}$$