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whats 8 to the power of 2015?

 Jun 16, 2015

Best Answer 

 #2
avatar+99214 
+10

$${{\mathtt{8}}}^{{\mathtt{2\,015}}} \approx \infty$$

 

The calculator did not help too much anon.    

The answer is big but it is not infinity anon :)

Let

$$\\y=8^{2015}\\\\
log(y)=log(8^{2015})\\\\
log(y)=2015log(8)\\\\$$

 

$${\mathtt{2\,015}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{8}}\right) = {\mathtt{1\,819.726\: \!323\: \!788\: \!766\: \!152\: \!5}}$$

 

$$\\y=10^{1819.7263237887661525}\\\\
y=10^{1819}*10^{0.7263237887661525}\\\\$$

 

$${{\mathtt{10}}}^{{\mathtt{0.726\: \!323\: \!788\: \!766\: \!152\: \!5}}} = {\mathtt{5.325\: \!051\: \!211\: \!327\: \!235\: \!4}}$$

 

so

 

$$\\8^{2105}\approx 5.32505\times 10^{1819}$$

.
 Jun 16, 2015
 #1
avatar
0

Try the calculator

 Jun 16, 2015
 #2
avatar+99214 
+10
Best Answer

$${{\mathtt{8}}}^{{\mathtt{2\,015}}} \approx \infty$$

 

The calculator did not help too much anon.    

The answer is big but it is not infinity anon :)

Let

$$\\y=8^{2015}\\\\
log(y)=log(8^{2015})\\\\
log(y)=2015log(8)\\\\$$

 

$${\mathtt{2\,015}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{8}}\right) = {\mathtt{1\,819.726\: \!323\: \!788\: \!766\: \!152\: \!5}}$$

 

$$\\y=10^{1819.7263237887661525}\\\\
y=10^{1819}*10^{0.7263237887661525}\\\\$$

 

$${{\mathtt{10}}}^{{\mathtt{0.726\: \!323\: \!788\: \!766\: \!152\: \!5}}} = {\mathtt{5.325\: \!051\: \!211\: \!327\: \!235\: \!4}}$$

 

so

 

$$\\8^{2105}\approx 5.32505\times 10^{1819}$$

Melody Jun 16, 2015

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