+0

# what is 9 to the power of 999

0
572
3

What is 9 to the power of 999?

Guest Mar 9, 2015

#1
+81022
+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
+81022
+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
+91451
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
+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

### 5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details