Question

O conjunto solução da equação log2 (x-3) - log4 (x-3) = 3 é:
a)61
b)65
c)69
d)60
e)67

Answer 1

$\log_{2}(x-3)-\log_{4}(x-3)=3$
$\log_{2}(x-3)-\log_{2^{2}}(x-3)=3$
$\log_{2}(x-3)- \frac{1}{2}\log_{2}(x-3)=3$
$\log_{2}(x-3)-\log_{2} (x-3)^{ \frac{1}{2} }=3$
$\log_{2} \frac{(x-3)}{ (x-3)^{ \frac{1}{2} } }=3$
$\log_{2}(x-3)^{1- \frac{1}{2} }=3$
$\log_{2}(x-3)^{ \frac{1}{2} }=3$
$\log_{2} \sqrt{x-3}=3$
$\sqrt{x-3}= 2^{3}$
$\sqrt{x-3}=8$
$(\sqrt{x-3})^{2}= 8^{2}$
$x-3=64$
$x=64+3$
$x=67$ (Alternativa E)