Question

sendo log 2=0,3; log 3=0,5 e log 5=0,7,calcule:
 
 a) log de 600 na base 8
 
 b) log de 60 na base 2                                                                                                                                  
        

Answer 1

Olá Gabi,

vamos utilizar as seguintes propriedades de log:

$logbc~\to~log(b*c)~\to~logb+logc\\ logb^k~\to~k*logb\\\\ log_cb~\to~ \dfrac{logb}{logc}$

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$log_8600= \dfrac{log600}{log8}\\\\\\ log_8600= \dfrac{log(2^3*3*5^2)}{log2^3}\\\\\\ log_8600= \dfrac{log2^3+log3+log5^2}{log2^3}\\\\\\ log_8600= \dfrac{3*log2+log3+2*log5}{3*log2}\\\\\\ log_8600= \dfrac{3*0,3+0,5+2*0,7}{3*0,3}\\\\\\ log_8600= \dfrac{0,9+1,9}{0,9}\\\\\\ log_8600= \dfrac{2,8}{0,9}\\\\\\ \boxed{log_8600\approx3,11}$

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$log_260= \dfrac{log60}{log2}\\\\\\ log_260= \dfrac{log(2^2*3*5)}{log2}\\\\\\ log_260= \dfrac{log2^2+log3+log5}{log2}\\\\\\ log_260= \dfrac{2*log2+log3+log5}{log2}\\\\\\ log_260= \dfrac{2*0,3+0,5+0,7}{0,3}\\\\\\ log_260= \dfrac{1,8}{0,3}\\\\\\ \boxed{log_260=6}$


Espero ter ajudado e tenha ótimos estudos =))