Question

Oblicz:

2log5(5)+3log2(4)=

4log2(jedna ósma)+log3(27)=

dla jednej wartości x log8(x^2-1)=2/3

Answer 1

 

 

 

 

 

 

Answer 2

2 log 5 [ 5 ] + 3 log 2 [ 4 ] = 2* 1 + 3*2 =2 + 6 = 8

4 log 2 [ 1/8 ] + log 3 [ 27 ] = 4* ( -3) + 3 = -12 + 3 =  - 9

log 8 [ x^2 - 1 ] =  2/3

Założenie: x^2 - 1 > 0

log 8 [ x^2 - 1  ] = 2/3 <= >  x^2 - 1 = 8  ^(2/3) <= > x^2 - 1 = [ 8^2]^)1/3) < =>

<=> x^2 - 1 = 64^ (1/3)  <=> x^2 - 1 = 4 <=> x^2 = 5 < = > x = p(5)

 

p(5)  - pierwiastek kwadratowy z 5