(log以4为底3的对数+log以8为底3的对数)×lg2⼀lg3

2024-11-20 18:32:15

推荐回答（5个）

回答1：

换底公式
原式=(lg3/lg4+lg3/lg8)×lg2/lg3
=(lg3/2lg2+lg3/3lg2)×lg2/lg3

=(1/2+1/3)×lg3/lg2×lg2/lg3

=5/6

回答2：

log4 3+log8 3 ×lg2/lg3
=lg3/lg 4 * lg2/lg3 + lg3/lg8 xlg2/lg3
=lg3/lg 2^2 * lg2/lg3 + lg3/lg2^3 xlg2/lg3
=1/2 +1/3
=5/6

回答3：

=(1/2*log以2为底3的对数+1/3*log以2为底3的对数)×lg2/lg3
=5/6*log以2为底3的对数×lg2/lg3
=5/6*lg3/lg2*lg2/lg3
=5/6

回答4：

（㏒43+㏒83）㏑2/㏑3
=(㏒2×23+㏒2×2×23）㏑2/㏑3
=(1/2㏒23+1/3㏒23) ㏑2/㏑3
=(5/6㏒23)·㏑2/㏑3
=5/6㏒23·㏒32
=5/6

回答5：

5/6