若log3[log4(log5a)

/>2007*log5(1)+log4(27)*log3(4)=2007*0+(lg27/lg4)*(lg3/lg4)=lg27/lg3=lg3³/lg3=3lg3/lg3=3

换成以10为底的对数,lg3/lg2*lg4/lg3*lg5/lg4*lg2/lg5=1

log2(3)*log3(4)*log4(5)*log5(2)=log2(3)*log3(2^2)*log2^2(5)*log5(2)=log2(3)*2log3(2)*1/2*log2(5)*log

1、logaC×logcA=logaC×(1/logaC)=12、log23×log34×log45×log52=[1/(log32)]×2log32×[1/(log54)]×log52=2×[1/2

原式=(ln2+ln3+ln4+ln5)/ln11=ln120/ln11=log11(120)11

原式=lg25/lg4-2lg10/lg4+lg9/lg2×lg√5/lg3×lg2/lg5=(2lg5)/(2lg2)-2/(2lg2)+(2lg3)/lg2×(½lg5)/lg3×lg2

log(a)(b)=log(c)(b)/log(c)(a)原式=log2(3)/log2(x)+log2(4)/log2(x)+log2(5)/log2(x)=log2(60)/log2(x)=log

=(lg4/lg3)(lg5/lg4)(lg8/lg5)(lg9/lg8)=2

log5^a这个的意思应该是以5为底的loga吧……应该不是5的a次方吧~要不就没有底数了……〔log4（log5^a）〕=〔log3（log5^b）〕=1log5^a=4,log5^b=3,上面两个

log4(log5a)=1log5a=4a=5^4=625同理,b=5^3所以a/b=5

由换底公式：左式=log3(x),右式=log8(2)=1/3所以,log3(x)=1/3得：x=3^(1/3)祝你开心!希望能帮到你,如果不懂,请追问,祝学习进步!O(∩_∩)O再问：怎么知道log

log2(3)*log3(4)*log4(5)*log5(6)*log6(7)*log7(8)=(lg3/lg2)(lg4/lg3(*.lg8/lg7;=lg8/lg2=log2(8)=3

(log23/log24+log23/log28)(log35/log33+log35/log39)(log52/log55+log52/log525)=[(5log23)/6][(3log35)/2

1、log23*log34*log45*log52=lg2/lg3xlg3/lg4xlg4/lg5xlg5/lg2（换底公式）=1（约分）2.(log43+log83)*(log32+log92)中间

求值log5[log4(log3x)]=0解方程log4(log3x)=5^0=1log₃x=4¹=4x=3⁴=81证明：log5[log4(log381)]log5

log23·log34·log45·log52=lg3/lg2*lg4/lg3*lg5/lg4*lg2/lg5=1再问：用换底公式？再答：嗯，都换成以10为底的log23=lg3/lg2用e为底的ln

∵log5底(log4底(log3底a))=0=log5底(1)∴log4底(log3底a)=1=log4底(4)∴log3底a=4∴a=3^4

2^[log2(3)*log3(4)*log4(5)*log5(6)*log6(7)*log7(8)]=(2^log2(3))*log3(4)*log4(5)*log5(6)*log6(7)*log7

运用换底公式得：原式=lg4/lg3*lg5/lg4*lg6/lg5*...*lg81/lg80=lg81/lg3=4lg3/lg3=4

M=9