Question

Sabendo que log ca = 6,42 ; log cb = 4,21 ; log cd = 2,31 determine log c [ (a 2.b 5) / (b 2.d 6) ]
A.
21,32

B.
25,61

C.
39,33

D.
11,61

E.
14,82

Answer 1

$\log_c\left(\dfrac{a^2b^5}{b^2d^6}\right)=\\\\\log_c(a^2b^5)-\log_c(b^2d^6)=\\\\\log_c(a^2)+\log_c(b^5)-(\log_c(b^2)+\log_c(d^6))=\\\\2\log_c(a)+5\log_c(b)-2\log_c(b)-6\log_c(d)=\\\\2(6.42)+5(4.21)-2(4.21)-6(2.31)=\\\\12.84+21.05-8.42-13.86=\\\\\boxed{11.61}$