Question

Proszę o rozpisywanie obliczeń, nie tylko sam wynik.

Ćw. 1.

a. log₂ 32

b. log₂ 2

c. log₂ 1

d. log₂ ¹/₂

e. log₂ ¹/₆₄

f. log₂ √2

g. log₂√8

h. log₂ ∛4

Ćw. 2

a. log₃ 81

b. log₃ ¹/₉

c. log₃ ¹/√3

d. log₉ 3

e. log₇ 7√7

f. log ½ ⅛

g. log½ 16

h. log₆ ∛36

Answer 1

Prosze bardzo mam nadzieje ze pomoglam;]

Answer 2

loga b = c  wtedy gdy  a^c = b

 

Ćw. 1.

a.

log₂ 32 = x

2^x = 32

2^x = 2^5

x = 5

log₂ 32 = 5

 

b.

log₂  2 = x

2^x = 2^1

x = 1

log₂  2 = 1

 

c.

log₂ 1 = x

2^x = 1

2^x = 2^0

x = 0

 

d.

log₂ ¹/₂ = x

2^x = 1/2

2^x = 2^(-1)

x = - 1

 

e.

log₂ ¹/₆₄ = x

2^x = 1/64

2^x = 64^(-1)

2^x = (2^6)^(-1)

2^x = 2^(-6)

x = -6

 

f. 

log₂ √2 = x

2^x = √2

2^x = 2^(1/2)

x = 1/2

 

g. log₂√8 = x

2^x = √8

2^x = (2^3)^(1/2)

2^x = 2^(3/2)

x = 3/2

 

h. log₂ ∛4 = x

2^x = ∛4

2^x = 4^(1/3)

2^x = (2^2)^(1/4)

2^x = 2^(1/2)

x = 1/2

 

Ćw. 2

a.

log₃ 81 = x

3^x = 81

3^x = 3^4

x = 4

 

b.

log₃ ¹/₉ = x

3^x = 1/9

3^x = 3^(-2)

x = -2

 

c.

log₃ ¹/√3 = x

3^x = (√3)^(-1)

3^x = 3^(-1/3)

x = -1/3

 

d. log₉ 3 = x

9^x = 3

(3^2)^x = 3^1

2x = 1

x = 1/2

 

e. log₇ 7√7 = x

7^x = 7√7

7^x = 7 * 7^(1/2)

7^x = 7^(3/2)

x = 3/2

 

f.  log ½ ⅛ = x

(1/2)^x = 1/8

(1/2)^x = (1/2)^3

x = 3

 

g. log½ 16 = x

(1/2)^x = 16

2^(-x) = 2^4

-x = 4

x = -4

 

h. log₆ ∛36 = x

6^x = 36^(1/3)

6^x = 6^(2/3)

x = 2/3