Si [tex]log_2(a+b)=4[/tex] y [tex]log_2(a-b)=6[/tex] , entonces [tex]log_4(a^2-b^2)=[/tex]
A)24
B)12
C)6
D)5
E) 10
A)24
B)12
C)6
D)5
E) 10
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Log(2) (a+b) = 4
Log(2) (a-b) = 6
Piden : Log(4) (a²-b²)
____
Log(2) (a+b) = 4 → a+b = 16
Log(2) (a-b) = 6 → a-b = 64
____
a+b = 16
a-b = 64
Multiplicando ambas ecuaciones queda :
a²-b² = 1024
Piden :
Log(4) (a²-b²)
Log(4) (1024) = 5
Respuesta = 5
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