Question

Oblicz x, gdy: a) logx4=2, logx1/9=1, logx16/9=2, logx1/4=-1 b) log2x^2=2, log2x^2=-4

Answer 1

a)

logx4=2,

x^2 = 4

x = 2  lub  x = -2  

 

logx1/9=1,

x^1 = 1/9

x = 1/9  

 

logx16/9=2,

x^2 = 16/9

x = 4/3   lub  x = -4/3  

 

logx1/4=-1

x^(-1) = 1/4

1/x = 1/4

x = 4  

 

b) log2x^2=2,

2^2 = x^2

x = 2  

 

log2x^2=-4

2^(-4) = x^2

(2^2)^(-2)=x^2

x^2 = 4^(-2)

x^2 =(1/4)^2

x = 1/4  

Answer 2

a)

 

x = 2, x = -2 bo 2^2 = 4 i (-2)^2 = 4

 

 x = 1/9, bo (1/9)^1 = 1/9

 

 x = 4/3, x = -4/3 bo (4/3)^2 = 16/9 i (-4/3)^2 = 16/9

 

x = 4, bo 4^(-1) = 1/4

 

 

 

 

b) log2x^2=2

 

2^2 = x^2

 

x= 2

 

 

log2x^2=-4

 

x^2 = (1/4)^2

 

x= 1/4