Question

Usando, aproximadamente, log 2 = 0,301; log 3 = 0,477 ; log 5 = 0,699 e log 7 = 0,845 , fatore e aplique as propriedades logarítmicas para calcular o valor do log2 8400:​

Answer 1

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf8400&\sf2\\\sf4200&\sf2\\\sf2100&\sf2\\\sf1050&\sf2\\\sf525&\sf3\\\sf175&\sf5\\\sf35&\sf5\\\sf7&\sf7\\\sf1\end{array}\\\sf8400=2^4\cdot3\cdot5^2\cdot7\\\sf \log_28400=\dfrac{\log8400}{\log2}\\\\\sf\log_28400=\dfrac{\log(2^4\cdot3\cdot5^2\cdot7)}{\log2}\\\\\sf \log_28400=\dfrac{\log2^4+\log3+\log5^2+\log7}{\log2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\log_28400=\dfrac{4\log2+\log3+2\log5+\log7}{\log2}\\\\\sf\log_28400=\dfrac{4\cdot0,301+0,477+2\cdot0,699+0,845}{0,301}\\\\\sf \log_28400=\dfrac{1,204+0,477+1,398+0,845}{0,301}\\\\\sf \log_28400=\dfrac{3,924}{0,301}\\\\\sf \log_28400=13,03\end{array}}$