作业帮1、log下标3 2(log下标4 3+log下标8 3)2、log下标1/3 √27+log下标27 1/3
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1、log下标3 2(log下标4 3+log下标8 3)2、log下标1/3 √27+log下标27 1/3
1、log下标3 2(log下标4 3+log下标8 3)
2、log下标1/3 √27+log下标27 1/3
1、log下标3 2(log下标4 3+log下标8 3)2、log下标1/3 √27+log下标27 1/3
1,用换底公式,都换成以3为底的对数.
log3(2)[log4(3)+log8(3)]
=log3(2)[1/log3(4)+1/log3(8)]
=log3(2)[1/2log3(2)+1/3log3(2)]
=1/2+1/3
=5/6
2.用换底公式,都换成以3为底的对数.
log1/3(√27)+log27(1/3)
=log3(√27)/log3(1/3)+log3(1/3)/log3(27)
=(3/2)/(-1)+(-1)/3
=-3/2-1/3
=-11/6
log下标3 2(log下标4 3+log下标8 3)
是log下标3 2^(log下标4 3+log下标8 3)吧？
log下标3 2^(log下标4 3+log下标8 3)
=log下标3 2*(ln3/ln4+ln3/ln8)
=log下标3 2(ln3/ln4+1/2*ln3/ln4)
=log下标3 2*3/2*(ln3/ln4)
=ln2...
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log下标3 2(log下标4 3+log下标8 3)
是log下标3 2^(log下标4 3+log下标8 3)吧？
log下标3 2^(log下标4 3+log下标8 3)
=log下标3 2*(ln3/ln4+ln3/ln8)
=log下标3 2(ln3/ln4+1/2*ln3/ln4)
=log下标3 2*3/2*(ln3/ln4)
=ln2/ln3*2*ln3ln2
=2
log下标1/3 √27+log下标27 1/3
=-log下标3 3^(3/2)+1/3*log下标3 1/3
=-3/2-1/3=-1
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1.原式=(lg2/lg3)*(lg3/lg4-lg3/lg8)=lg2*(1/(2lg2)+1/(3lg2))=1/2+1/3=5/6
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