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2^(x)*4^(3x)= 10

 21.10.2016
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2^(x)*4^(3x)= 10   x=?

 

\(\begin{array}{|rcll|} \hline 2^{x}\cdot 4^{3x} &=& 10 \\ 2^{x}\cdot (4^{3})^x &=& 10 \quad &| \quad 4^{3} = 64\\ 2^{x}\cdot 64^x &=& 10 \\ (2\cdot 64)^{x} &=& 10 \\ 128^{x} &=& 10 \quad &| \quad \log_{10}{()}\\ \log_{10}{( 128^{x})} &=& \log_{10}{(10)} \quad &| \quad \log_{10}{(10)} = 1\\ \log_{10}{( 128^{x})} &=& 1\\ x\cdot \log_{10}{( 128 )} &=& 1\quad &| \quad : \log_{10}{( 128 )}\\ x &=& \frac{1} {\log_{10}{( 128 )}} \\ \mathbf{x} &\mathbf{=}& \mathbf{0,47456115641} \\ \hline \end{array}\)

 

laugh

 21.10.2016

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