Tính: a) A=25^log 5 6 + 49 log 7 8 -3/3^1+ log 9 4 + 4 ^2-log 2 3+5 ^ log 125 27
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23/10/2024
Tính:
a) A=25log56+49log78−331+log94+42−log23+5log12527;
b) B=36log65+101−log2−3log936log2(log2√4√2);
c) C=log14(log34⋅log23);
d) D = log4 2 . log6 4 . log8 6.
Trả lời
a) A=25log56+49log78−331+log94+42−log23+5log12527
=(52)log56+(72)log78−33⋅3log94+424log23+5log53(33)=(5log56)2+(7log78)2−33⋅3log32(22)+42(22)log23+513⋅3⋅log53
=62+82−33⋅3log32+42(2log23)2+5log53=36+64−33⋅2+4232+3=976+169+3=97979=9.
b) B=36log65+101−log2−3log936log2(log2√4√2)
=(62)log65+1010log2−3log32(62)log2(log2√214)=(6log65)2+102−312⋅2⋅log36log2(log2218)
=52+5−3log36log2(18)=25+5−6log22−3=24−3=−8.
c) C=log14(log34.log23)
=log2−2(log322⋅log23)=−12log2(2log32⋅log23)=−12log2(2log32⋅1log32)=−12log22=−12.
d) D = log4 2 . log6 4 . log8 6
=log42⋅log44log46⋅log46log48=log42⋅log44log48
=log42⋅log84=log84⋅log42
=log82=log232=13log22=13.