1.Oblicz:
a) log 40 - 2×log 2=log40-log2²=log40-log4=log(40:4)=log10=1
b) 2×log 4 - 4×log 2=log4²-log2⁴=log16-log16=log(16:16)=log1=0
c) log 36 - 2×log 6 + 3×log 1=log36-log6²+log1³=log36-log36+log1=log(36:36)+log1=log1+log1=log(1*1)=log1=0
1.Oblicz:
a) log₃9√₂₇=log₃(3²*(3³)^(1/2))=log₃(3²*3^(3/2))=log₃(3^(7/2))=(7/2)log₃3=(7/2)*1=(7/2)=3,5
b) log√₁₀10=log(10^(1/2)*10)=log(10^(3/2))=(3/2)log10=(3/2)*1=(3/2)=1,5
c)log[ 10√₁₀/1000]=log[10^(3/2)/10³]=log[10^(-3/2)]=(-3/2)log10=(-3/2)*1=(-3/2)=-1,5
d) 2log₄ ⅓ - log₄ (1/18)=log₄(1/3)²-log₄(1/18)=log₄(1/9)-log₄(1/18)=log₄[(1/9):(1/18)]=log₄[(1/9)*(18/1)]=log₄[18/9]=log₄2=1/2
2. Zapisz w prostszej postaci:
a) log 5 + log 2= log(5*2)=log10=1
b) log 80 - 3log 2=log80-log2³=log80-log8=log(80:8)=log10=1
c) log 5×log₅ 10=log5x(log10/log5)=log10=1
d) log₆ 2 + log₆30 - log₆ 10=log₆(2*30)-log₆10=log₆60-log10=log₆(60:10)=log₆6=1
