(log8 9/log2 3)=?

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(log8 9/log2 3)=?
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(log8 9/log2 3)=?
(log8 9/log2 3)=?

(log8 9/log2 3)=?
方法一
(log8 9/log2 3)
=(lg9/lg8)/(lg3/lg2)
=(2lg3/3lg2)/(lg3/lg2)
=(2/3)*(lg3/lg2)/(lg3/lg2)
=2/3
方法二
(log8 9/log2 3)
=log2^3 3^2/log2 3
=(2/3)log2 3/log 2 3
=2/3
logm^a n^b
=(b/a)logm n

(log8 9/log2 3)=(log8 3^2/log2 3)=(2log8 3/log2 3)=(2log3 2/log3 8)=log8 2

用换底公式
(log8 9/log2 3)
=(lg9/lg8)/(lg3/lg2)
=(2lg3/3lg2)/(lg3/lg2)
=(2/3)*(lg3/lg2)/(lg3/lg2)
=2/3