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# whats 8 to the power of 2015?

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542
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whats 8 to the power of 2015?

Jun 16, 2015

#2
+101733
+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
0

Try the calculator

Jun 16, 2015
#2
+101733
+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

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

Melody Jun 16, 2015