Hej pomozecie mam zadanie z logarytmow pomoze ktos?
Musza byc wszystkie oblicznie prosze:)
1zad
a)log₃x=-1
b)log₅x=3
c)log½x=-2
d)log⅓x=-½
e)log₂x=-2/3
f)log₄x=0
g)log₂x=10
h)log(dwa pierwiastki z dwoch)x=-3
2zad
a)log(x Na dole)25=2
b)log(x na dole)81=4
c)log(x na dole)3=½
d)log(x na dole)2=½
e)log(x na dole)1/9=-2
f)log(x na dole)64=-3
g)log(x na dole)27=3
h)log(x na dole)36=-2
Z gory bardzo dziekuje:)

1

Odpowiedzi

Najlepsza Odpowiedź!
  • Użytkownik Zadane
2010-01-01T20:29:37+01:00
Ad 1.
a)log₃x=-1
x = 3^(-1) = 1/3

b)log₅x=3
x = 5^3 = 125

c)log½x=-2
x = (1/2)^-2 = 2^2 = 4

d)log⅓x=-½
x = (1/3)^(-1/2) = 3^(1/2) = √3

e)log₂x=-2/3
x = 2^(-2/3) = (1/2)^(2/3) = 1/∛4

f)log₄x=0
x = 4^0 = 1

g)log₂x=10
x = 2^10 = 100

h)log(dwa pierwiastki z dwóch)x=-3
x = 2√2^(-3) = √8^(-3) = 2^(-1) = 1/2


Ad 2.
a)log(x na dole)25=2
x^2 = 25
x = 5

b)log(x na dole)81=4
x^4 = 81
x = 3

c)log(x na dole)3=½
x^(1/2) = 3
√x = 3
x = 9

d)log(x na dole)2=½
x^(1/2) = 2
√x = 2
x = 4

e)log(x na dole)1/9=-2
x^(-2) = 1/9
1/x^2 = 1/9
x^2 = 9
x = 3

f)log(x na dole)64=-3
x^(-3) = 64
x^(-1) = 4
1/x = 4
x = 1/4

g)log(x na dole)27=3
x^3 = 27
x = 3

h)log(x na dole)36=-2
x^(-2) = 36
x^(-1) = 6
1/x = 6
x = 1/6