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What is 9 to the power of 999?

Guest Mar 9, 2015

Best Answer 

 #1
avatar+81023 
+10

We can evaluate   999log(9)  = 953.288

This equals about

 (10953)*10.288 =

10953 * 1.942 =

1.942 x 10953

All in all......a really big number.....1942 followed by 950 zeros.......!!! {more or less}

 

  

CPhill  Mar 9, 2015
Sort: 

3+0 Answers

 #1
avatar+81023 
+10
Best Answer

We can evaluate   999log(9)  = 953.288

This equals about

 (10953)*10.288 =

10953 * 1.942 =

1.942 x 10953

All in all......a really big number.....1942 followed by 950 zeros.......!!! {more or less}

 

  

CPhill  Mar 9, 2015
 #2
avatar+91462 
0

Thanks Chris,

I am only just getting the hang of these.    

It is a tricky way of finding high powers that the calc cannot find on its own. 

If you can do a calc that the calc cannot do on its own does that kind of make you = 42?

Melody  Mar 9, 2015
 #3
avatar+18829 
+5

What is 9 to the power of 999 ?

change of basis: 9 to 10

$$b_1^{ e_1 } = b_2^{ e_2 } \quad | \quad \ln() \\
e_1 \cdot \ln{(b_1)} = e_2 \cdot \ln{(b_2)} \\\\
e_2 = e_1 \cdot \dfrac{ \ln{(b_1)} } { \ln{(b_2)} } \\
\boxed{
b_1^{ e_1 } = b_2^{ e_1
\left(
\cdot \dfrac{ \ln{(b_1)} } { \ln{(b_2)} }
\right)
}}\\\\
\small{\text{
$
b_1 = 9 \qquad e_ 1 = 999 \qquad b_2 = 10
$
}} \\\\
\small{\text{
$
9^{999} = 10^{999
\left(
\cdot \dfrac{ \ln{(9)} } { \ln{(10)} }
\right)
}
$
}} \\\\
\small{\text{
$ 9^{999} = 10^{999 \cdot( 0.95424250944 ) } $ }} \\
\small{\text{
$ 9^{999} = 10^{953.288266930} $
}} \\
\small{\text{
$ 9^{999} = 10^{0.288266930}\cdot 10^{953} $
}} \\
\small{\text{
$ 9^{999} = 1.94207916858
\cdot 10^{953} $
}}$$

heureka  Mar 9, 2015

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