利用对数的换底公式化简[log4（3）+log8(3)]*[log3(2)+log9(2)]括号中的数是真数若以2为底数，

利用对数的换底公式化简[log4（3）+log8(3)]*[log3(2)+log9(2)]括号中的数是真数若以2为底数，
利用对数的换底公式化简
[log4（3）+log8(3)]*[log3(2)+log9(2)]
括号中的数是真数
若以2为底数，

利用对数的换底公式化简[log4（3）+log8(3)]*[log3(2)+log9(2)]括号中的数是真数若以2为底数，
[log4（3）+log8(3)]*[log3(2)+log9(2)]
=((log3/log4)+(log3/log8))*((log2/lg3)+(log2/log9))
=((1/2)(log3/log2)+(1/3)(log3/log2))*((log2/lg3)+(1/2)(log2/log3))
=((1/2)+(1/3))*(1+(1/2))
=5/4
[log4（3）+log8(3)]*[log3(2)+log9(2)]
=((1/2)log2(3)+(1/3)log2(3))*((1/log2(3))+(1/2)log2(3))
=((1/2)+(1/3))*(1+(1/2))
=5/4

=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=[(1/2+1/3)lg3/lg2][(1+1/2)lg2/lg3]
=(1/2+1/3)(1+1/2)
=5/4

写成除法
=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=[(1/2+1/3)lg3/lg2][(1+1/2)lg2/lg3]
=(1/2+1/3)(1+1/2)
=5/4

原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
=[(1/2+1/3)lg3/lg2][(1+1/2)lg2/lg3]
=(1/2+1/3)(1+1/2)
=5/4