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# 5.478 to the power 967?

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how do i get the answer to: 5.478 to the power 967?

Guest Oct 12, 2017
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how do i get the answer to: 5.478 to the power 967?

$$5.478^{967} = 1.7680762752393208561357751278000043204596021262381226... \times 10^{714}$$

$$\begin{array}{|rcll|} \hline z &=& 5.478^{967} \quad & | \quad \log_{10} \\ \log_{10}(z) &=& \log_{10} ( 5.478^{967} ) \\ \log_{10}(z) &=& 967 \cdot \log_{10} ( 5.478 ) \\ \log_{10}(z) &=& 967 \cdot 0.73862202792 \\ \log_{10}(z) &=& 714.247500997 \quad & | \quad 10^{()} \\ z &=& 10^{714.247500997} \\ &=& 10^{714+0.247500997} \\ &=& 10^{714}\cdot 10^{0.247500997} \\ &=& 10^{0.247500997} \cdot 10^{714}\\ z &=& 1.768076275239\ldots \cdot 10^{714}\\\\ \mathbf{5.478^{967}} &\mathbf{=}& \mathbf{1.768076275239\ldots \cdot 10^{714}} \\ \hline \end{array}$$

heureka  Oct 12, 2017