Question

UCSal - Se 12n+1 = 3n+1 . 8 , então log2 n é igual a:
a) -2 
*b) -1 
c) 1/2 
d) 1 
e) 2

Answer 1

$a^{n}/b^{n}=(a/b)^{n}$
$(x^{a})^{b}=x^{(a*b)}$
$log_{n}(n)=1$
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$12^{(n+1)}=3^{(n+1)}*8$
$12^{(n+1)}/3^{(n+1)}=8$
$(12/3)^{(n+1)}=2^{3}$
$4^{(n+1)}=2^{3}$
$(2^{2})^{(n+1)}=2^{3}$
$2^{(2n+2)}=2^{3}$

Bases iguais, iguale os expoentes:

$2n + 2= 3$
$2n=3-2$
$2n=1$
$n=1/2$
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$log_{2}(n)=log_{2}(1/2)=log_{2}(2^{-1})=(-1)*log_{2}(2)=(-1)*1=-1$