Respostas
Resposta:
log
x
8
1
+
log
2x
8
1
+
log
4x
8
1
=2
1/\frac{\log8}{\log x}+1/\frac{\log8}{\log 2x}+1/\frac{\log8}{\log 4x}=21/
logx
log8
+1/
log2x
log8
+1/
log4x
log8
=2
\frac{\log x}{\log 8}+\frac{\log 2x}{\log 8}+\frac{\log 4x}{\log8}=2
log8
logx
+
log8
log2x
+
log8
log4x
=2
\frac{\log x+\log2x+\log4x}{\log8}=2
log8
logx+log2x+log4x
=2
\log x+\log2x+\log4x=2\log8logx+log2x+log4x=2log8
\log(x.2x.4x)=\log8^2log(x.2x.4x)=log8
2
x.2x.4x=8^2x.2x.4x=8
2
8x^3=648x
3
=64
x^3=\frac{64}{8}x
3
=
8
64
x^3=8x
3
=8
x=\sqrt[3]{8}x=
3
8
x=2x=2
Apenas 1 condição de existência: x=2
Gabarito: a)
Resposta:
x = 3 (Alternativa C)
Explicação passo-a-passo:
2 log11 (x-1) = log11 (x² - 5), x e (√5, +∞)
log11 ((x-1)²)= log11 (x²-5)
(x-1)² = x²-5
x²-2x=1= x² -5
-2x+1= -5
-2x= -5-1
-2x=-6
x= 3