Question

como resolver , Sabendo que logca = 6,42 ; logcb = 4,21 ; logcd = 2,31 determine
logc [ (a2.b5) / (b2.d6) ] , tentei resolver e deu 20,24 porém as alternativas são
A.
21,32

B.
14,82

C.
11,61

D.
39,33

E.
25,61

Answer 1

Boa tarde!

Solução!

$logca=6.42\\\\\\\ logcb=4.21\\\\\\\ logcd=2.31$

Propriedade dos logaritmos.

$log(t.v)= log(t)+log(v)~~Produto\\\\\\\ log \dfrac{t}{v} =log(t)-log(v)~~~Quociente\\\\\\\\ logt^{v}=vlogt~~Potencia$


$logc= \bigg(\dfrac{a^{2} .b^{5} }{b^{2}.d^{6}}\bigg)\\\\\\ \dfrac{logca^{2} +logcb^{5} }{logcb^{2}+logcd^{6} } \\\\\\\ \dfrac{2logca+5logcb }{2logcb+6logcd } \\\\\\\ \dfrac{2(6.42)+5(4.21) }{2(4.21)+6(2.31) }$


$\dfrac{12.84+21.05 }{8.42+13.86 } \\\\\\\ \dfrac{33.89 }{22.28 }$


Observando as propriedades acima,fica assim:


$33.89-22.28=11.61$


$\boxed{Resp=11,61~~\boxed{Alternativa~~C}}$

Boa noite!
Bons estudos!