Question

Proszę o bezbłędne rozwiązaniezadań:

1. Oblicz x, gdy:

a)log3 x= -2

b) logx 4= 2

c) log3 x =0

d) logx 1/9 = 1

e)log1/3 x= -2

f) logx 16/9 = 2

2.Oblicz:

a) log4 + log25

b) 2log3 6 - log3 4

c) log8 + 3log5

d) log4 400 - 2log4 5

Answer 1

a]

3⁻²=x

x=1/9

b]

x²=4

x²=2²

x=2

c]

3⁰=x

x=1

d]

x¹=1/9

x=1/9

e]

(1/3)⁻²=3²=9

f]

x²=16/9

x=√16/9

x=4/3

2a]

log4+log25=log(4*25)=log₁₀100=x

10 do potegi x=100

x=2

b]

2log₃6-log₃4=log₃(36/4)=log₃9=2

c]

log8+3log5=log8+log5³=log(8*125)=log1000=log₁₀1000=3

d]

log₄400-2log₄5=log₄400-log₄25=log₄(400/25)=log₄16=2

Answer 2

1.

a)

log₃ x = -2

3⁻² = x

x = (1/3)²

x = 1/9

---------

b)

log_x (4) = 2

x² = 4 

x² = 2²

x = 2

-------

c)

log₃ x = 0

x = 3⁰

x = 1

-------

d)

log_x (1/9) = 1

x¹ = 1/9

x = 1/9

---------

e)

log⅓ (x) = -2

x = (1/3)⁻²

x = 3²

x = 9

-------

f)

log_x (16/9) = 2

x² = 16/9

x = 4/3

---------

 

2.

a)

log 4 + log 25 = log (4·25) = log 100 = 2,   bo 10² = 100

b)

2log₃ 6 - log₃ 4 = log₃ 6² - log₃ 4 = log₃ (36/4) = log₃ 9 = 2,   bo 3² = 9

c)

log 8 + 3log 5 = log 8 + log 5³ = log (8·125) = log 1000 = 3,   bo 10³ = 1000

d)

log₄ 400 - 2log₄ 5 = log₄ 400 - log₄ 5² = log₄ 400 - log₄ 25 = log₄ (400/25) = log₄ 16 = 2