a soma dos termos da sequência finita (logxx/10,logxx,logx10x,...,logx10000x),onde x ∈ IR₊ * - {1} e logx=0,6,vale:
resposta :21,0
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![log_{x} [ \frac{x}{10}.x.10x.100x.1000x.10000x]= log_{x} 10^{9}. x^{6} = \\ \\ log_{x} 10^{9} + log_{x} x^{6} =9. log_{x} 10+6. log_{x} x \\ \\ 9. \frac{log 10}{log x} +6.1=9. \frac{1}{0,6}+6=15+6=21](https://tex.z-dn.net/?f=+log_%7Bx%7D+%5B+%5Cfrac%7Bx%7D%7B10%7D.x.10x.100x.1000x.10000x%5D%3D+log_%7Bx%7D++10%5E%7B9%7D.+x%5E%7B6%7D++%3D+%5C%5C++%5C%5C++log_%7Bx%7D++10%5E%7B9%7D+%2B+log_%7Bx%7D+++x%5E%7B6%7D+%3D9.+log_%7Bx%7D+10%2B6.+log_%7Bx%7D+x+%5C%5C++%5C%5C+9.+%5Cfrac%7Blog+10%7D%7Blog+x%7D+%2B6.1%3D9.+%5Cfrac%7B1%7D%7B0%2C6%7D%2B6%3D15%2B6%3D21+ "log_{x} [ \frac{x}{10}.x.10x.100x.1000x.10000x]= log_{x} 10^{9}. x^{6} = \\ \\ log_{x} 10^{9} + log_{x} x^{6} =9. log_{x} 10+6. log_{x} x \\ \\ 9. \frac{log 10}{log x} +6.1=9. \frac{1}{0,6}+6=15+6=21")
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