a) log39=log332=2
b) log218=log2123=log21(21)−3=−3
c) log525=log552=log5((5)2)2=log5(5)2⋅2=log5(5)4=4
d) log813=log8134⋅14=log81(34)41=log818141=41
e) log8(42)=log8(22221)=log8221−2=log82−23=log823⋅(−21)=log8(23)−21=
=log88−21=−21
f) log3339=log3⋅33132=log31+3132=log334(32)34⋅43=log334(32⋅34)43=
=log334(334⋅2)43=log334(334)2⋅43=log334(334)23=23
g) log0,01100=log0,01(1001)−1=log0,01(0,01)−1=−1
h) log2(22)=log2(2⋅221)=log221+21=log2(23)=23
i) log33(271)=log33(331)=log33(31)3=log333−3=log33((33)3)−3=
=log33(33)3⋅(−3)=log33(33)−9=−9
j) log0,04(55)=log1004(5521)=log251521−1=log(51)2521=log5−2(5−2⋅(−21))21=
=log5−2(5−2)(−21)⋅21=log5−2(5−2)−41=−41