Question

a soma dos termos da sequência finita (logxx/10,logxx,logx10x,...,logx10000x),onde x ∈ IR₊ * - {1} e logx=0,6,vale:

resposta :21,0

Answer 1

Boa tarde

$log_{x} \frac{x}{10} + log_{x} x+ log_{x} 10x+ log_{x} 100x+ log_{x}1000x+ log_{x}10000x=$

$log_{x} [ \frac{x}{10}.x.10x.100x.1000x.10000x]= log_{x} 10^{9}. x^{6} = \\ \\ log_{x} 10^{9} + log_{x} x^{6} =9. log_{x} 10+6. log_{x} x \\ \\ 9. \frac{log 10}{log x} +6.1=9. \frac{1}{0,6}+6=15+6=21$