+0

# what is 9 to the power of 999

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696
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What is 9 to the power of 999?

Guest Mar 9, 2015

#1
+85726
+10

We can evaluate   999log(9)  = 953.288

(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:

#1
+85726
+10

We can evaluate   999log(9)  = 953.288

(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
+92215
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
+19207
+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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