Question

WItam.. mam garść zadań z LOGARYTMÓW.

zad.1
OBLICZ:
a) log₄40+log₄1/5 = ...
b) log4/9 z 8 - log4/9 z 27 = ...
c) log4 - log250 = ...

d) log₆24 + 2/3log₆27 - 1 = ...

zad.2
OBLICZ:
a) log₂1/1024
b) log⅓ z 81
c) log₀,₁0,01
d) log√₅5∛5
e) log₂8√2
f) 2^ log₂7

zad.3
OBLICZ X JEŚLI:
a) logx3=1/2
b) logx25=2
c) log₃x= -2
d) log1/2x= -2

Answer 1

zad.1)

 

log₄40+log₄1/5=log₄40*1/5=log₄8=log₄4*2=log₄4+log₄2=1+1/2=1½

 

b)log₄/₉ 27=log₄/₉ 8/27=log₄/₉(2/3)²=2log₄/₉ 2/3=2*1/2=1

 

c)log4-log250=log1000=3

 

d)log₆24+2/3log₆27-1=log₆6*4+2/3log₆3*9 -1=log₆6+log₆4+2/3log3³ -1=

 

 =1+log₆2²+6/3log₆3-1=1+2log₆2+2log₆3 -1=2(log₆2+log₆3)=2*log₆2*3=

 

=2log₆6=2*1=2

 

 

zad.2).

 

log₂1/1024=10

 

log₁/₃ 81=-4

 

c)log₀,₁0,01=2

 

d)log√₅ 5∛5=log√₅ 5²/₃=2/3log√₅ 5=2

 

e)log₂8√2=log₂8+log₂√2=3+1/2=3½

 

f)2^(log₂7)=7

 

zad.3).

 

a)log_{x} 3=1/2

         x=9

b)log_{x} 25=2

            x=5

 

c)log_{3} x=-2

                 x=1/9

 

log_{½} x=-2

              x=4