运用换底公式化简下列各式logaC×logcAlog23×log34×log45×log52(log43+log83)(log32+log92)
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运用换底公式化简下列各式logaC×logcAlog23×log34×log45×log52(log43+log83)(log32+log92)
运用换底公式化简下列各式
logaC×logcA
log23×log34×log45×log52
(log43+log83)(log32+log92)
运用换底公式化简下列各式logaC×logcAlog23×log34×log45×log52(log43+log83)(log32+log92)
logaC×logcA= (lgC/lga)×(lga/lgC)=1
log2 3 × log3 4 × log4 5 × log5 2
=(lg3/lg2)×(lg4/lg3)×(lg5/lg4)×(lg2/lg5)
=1
(log43+log83)(log32+log92)
=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=[(5/6)(lg3/lg2)][(3/2)(lg2/lg3)]
=5/4
1
1
5/4
logaC×logcA
=(lgC/lgA)(lgA/lgC)=1
log23×log34×log45×log52
=(lg3/lg2)(lg4/lg3)(lg5/lg4)(lg2/lg5)
=1
(log43+log83)(log32+log92)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=(1/2lg2+1/3lg2)(lg2+lg2/2)
=(1/2+1/3)(1+1/2)
=(5/6)(3/2)
=5/4
1、logaC×logcA= logaC×(1/logaC)=1
2、log2 3 × log3 4 × log4 5 × log5 2
=[1/(log3 2)]×2log3 2×[1/(log5 4)]×log5 2
=2×[1/2(log5 2)]×log5 2
=2×(1/2)
=1
logaC×logcA
=logmC/logmA*logmA/logmC
=1
log23×log34×log45×log52
=loga3/loga2*loga4/loga3*loga5/loga4*loga2/loga2
=1
(log43+log83)(log32+log92)
=(loga3/loga4+loga3/loga8)*...
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logaC×logcA
=logmC/logmA*logmA/logmC
=1
log23×log34×log45×log52
=loga3/loga2*loga4/loga3*loga5/loga4*loga2/loga2
=1
(log43+log83)(log32+log92)
=(loga3/loga4+loga3/loga8)*(loga2/loga3+loga2/loga3)
=[loga3/(2*loga2)+loga3/(3*loga2)]*[loga2/loga3+loga2/(2*loga3)]
设 loga3=m,loga2=n
则上式变为
=(m/2n+m/3n)*(n/m+n/2m)
=(1/2+1/3)*(1+1/2)
=5/6*3/2
=5/4
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