Question

log以2为底9的对数乘于log以3为底4的对数怎么算！在线等！

Answer 1

log以2为底9的对数乘于log以3为底4的对数怎么算！在线等！

换底公式
我喜欢ln
所以
log2(9)
=ln9/ln2
=ln(3^2)/ln2
=2*ln3/ln2
log3(4)
=ln4/ln3
=ln(2^2)/ln3
=2*ln2/ln3
log2(9)*log3(4)
=2*ln3/ln2*2*ln2/ln3
=2*2*(ln3/ln2*ln2/ln3)
=4*1
=4

log以2为底25的对数乘以log以3为底4的对数乘以log以5为底9的对数

log2(25)*log3(4)*log5(9)
=lg25/lg2*lg4/lg3*lg9/lg5 (换底公式)
=lg5^2/lg2*lg2^2/lg3*lg3^2/lg5
=2lg5/lg2*2lg2/lg3*2lg3/lg5
=2(lg5/lg2)*2(lg2/lg3)*2(lg3/lg5)
=8*1
=8

log以2为底3的对数乘与log以3为底4的对数乘与……log以2008为底2009的对数

log以2为底1/25的对数乘log以3为底数1/8的对数乘log以5为底数1/9的对数 =-log2(25) * log3(8) * log5(9) =-2log2(5) * 3log3(2) * 2log5(3) =-12*(lg5/lg2)(lg2/lg3)(lg3/lg5) =-12

log以4为底数27的对数乘log以5为底8的对数乘log以3为底25的对数

9.

log以2为底25的对数*log以3为底（2*根下2）的对数*log以3为底9的对数=

解：原式=lg25/lg2*lg2√2/lg3*2
=2lg5/lg2*3/2*lg2/lg3*2
=6lg5/lg3
=6log3 5

log以8为底9的对数，乘以log以9为底8的对数，等于？

log8(9)*log9(8)=(log9/log8)*(log8/log9)=1

log以3为底4的对数乘以log以4为底27的对数乘以log以2的3次方为底m的对数等于2求m的值

log3 4*log4 3³*log2³ m=2
log3 4*3log4 3*(1/3)log2 m=2
3*(1/3)log2 m=2
log2 m=2
m=4

设log以3为底4的对数,乘以log以8为底M的对数,等于log以4为底16的对数,那么M等于多少?

D
首先化减:
log8(M)*log3(4)=log4(16)=2
log8(M)=2/log3(4)=log3(9)/log3(4)
运用换底公式
log3(9)/log3(4)=log4(9)
所以log8(M)=log4(9)
即log2^3(M)=log2^2(9)
然后把底数的次方数提到前面
即1/3log2(M)=1/2log2(9)
log2(M)=3/2log2(9)=log2(9^(3/2))=log2(27)
M=27

log以2为底3的对数乘以log以9为底4的对数，要过程

=log2 3×log3² 2²
=log2 3×log3 2
=1

设log以3为底7的对数=a, log以2为底3的对数=b 则log以2为底7的对数=

答：
log3(7)=a，3^a=7
log2(3)=b，2^b=3
所以：(2^b)^a=7
所以：2^(ab)=7
所以：log2(7)=log2[2^(ab)]=ab
所以：log2(7)=ab