Question

Znajdź x :

a) log₃ x = 3log₃ 2 + 2log₃3

b) log₄ x = 3log₄ 5 - 2/3log₄4 + 1/3log₄2

c) log₅ x = 2log₅3 - 1/2log₅16 + 2/3log₅8

d) log₃x = log₃15 - 1/3log₃27 - 2log₃5 + log₃50

e) log₂x = log√₂ 2 - 1/2log₃4 + log₃6 + log₃3

Ma wyjść w :

a)72 b) 62,5 c)9 d) 10 e) 16

Answer 1

a)

log₃ x=3log₃2+2log₃3

log₃x=log₃8+log₃9

log₃x=log₃72

x=72

b)

log₄x=3log₄5-²/₃log₄4+¹/₃log₄2

log₄x=log₄125-log₄∛16+log₄∛2

log₄x=log₄(125·∛2/∛16)

log₄x=log₄(125/∛8)

log₄x=log₄62,5

x=62,5

c)

log₅x=2log₅3-0,5log₅16+²/₃log₅8

log₅x=log₅9-log₅4+log₅4

log₅x=log₅9

x=9

d)

log₃x=log₃15-¹/₃log₃27-2log₃5+log₃50

log₃x=log₃15-log₃3-log₃25+log₃50

log₃x=log₃10

x=10

e)

log₂x=log√₂2-0,5log₃4+log₃6+log₃3

log₂x=2-log₃2+log₃6+1

log₂x=3+log₃3

log₂x=3+1

log₂x=4

log₂x=log₂2⁴

log₂x=log₂16

x=16

Answer 2

a) 3log₃ 2 + 2log₃3  = log₃2³ + log₃3² =log₃8 + log₃9 = log₃(8 · 9) = log₃72
b) 3log₄ 5 - 2/3log₄4 + 1/3log₄2 = log₄5³ - log₄4^(2/3) + log₄2^(1/3) = log₄125 - log₄2^(4/3) + log₄2(1/3) = log₄(125·∛2:∛16)=log₄(125·∛(1/8)) = log₄(125·1/2) = log₄62,5
c) 2log₅3 - 1/2log₅16 + 2/3log₅8 = log₅3² - log₅16^(1/2) + log₅8^(2/3) = log₅9 - log₅4 + log₅4 = log₅(9*4:4) = log₅9
d) log₃15 - 1/3log₃27 - 2log₃5 + log₃50 = log₃12 - log₃27^(1/3) - log₃5² + log₃50 = log₃(15:3:25*50) = log₃10
e)  log√₂ 2 - 1/2log₃4 + log₃6 + log₃3 = 2 - log₃4^(1/2) + log₃6 + log₃3 = 2 + log₃(6*3:2) = 2 + log₃9 = 2+2 = 4
 
log₂x = 4
2^4 = x
x = 16