Question

1.Oblicz:
a)log2 8+ log1/2 4+ log9 81=
b)log 0,1+ log 1000+ log0,1 10=
c)log3 27- log4 2- log2 1/8=
d)log36 6+log16 4- log8 2=
2. Oblicz:
a)log6 2+ log6 18=
b)log 15- log 3/2=
c)log5 50- 1/2log5 4=
d)log6 4 +log6 27-log6 3=
e)log 1/2-log 25-log 2=
f)log5 10√5- log5 6+log5 3=

Answer 1

Zad1
a)log₂8+log₁/₂ 4+log₉81=log₂2³+log₂⁻¹2²+log₉9²=3log₂2-2log₂2+2log₉9=3-2+2=3
b)log0,1+log1000+log₀,₁10=log(0,1*1000)+log₁₀⁻¹10=log100-log10=2-1=1
c)log₃27-log₄2-log₂1/8=log₃3³-log₂²2-log₂2⁻³=3log₃3-1/2log₂2-(-3)log₂2=3-1/2+3= =5 1/2
d)log₃₆6+log₁₆4-log₈2=log₆²6+log₄²4-log₂³2=1/2log₂2+1/2 log₄4-1/3log₂2=1/2+1/2-1/3=1-1/3=2/3
zad2
a)log₆2+log₆18=log₆(2*18)=log₆36=2          ,
      bo 6²=36
b)log15-log3/2=log15/3/2=log15*2/3=log10=1
c)log₅50-1/2log₅4=log₅50-log₅4¹/²=log₅50og₅√4=log₅50-log₅2=log₅50/2=log₅25=2           bo 5²=25
d)log₆4+log₆27-log₆4+log₆27/3=log₆4+log₆9=log₆(4*9)=log₆36=2
e)log1/2 -log25-log2=log (1/2*1/25*1/2)=log1/100=-2
f)log₅10√5-log₅6+log₅3=log₅10+log₅5¹/²-log₅(2*3)+log₅3=log₅(2*5)+log₅5¹/²-[log₅2+log₅3)+log₅3=log₅2+log₅5+log₅5¹/²-log₅2-log₅3+log₅3=log₅5+1/2 log₅5=1+1/2=1 1/2