log4为底3的对数*log9为底2的对数+log2为底(4倍根号35)的对数(2)(log4为底3的对数+log8为底3的对数)(log3为底2的对数+log9为底2的对数)

问题描述:

log4为底3的对数*log9为底2的对数+log2为底(4倍根号35)的对数
(2)(log4为底3的对数+log8为底3的对数)(log3为底2的对数+log9为底2的对数)

1、
换底公式
原式=(lg3/lg4)(lg2/lg9)+log2(4)+log2(√35)
=(lg3/2lg2)(lg2/2lg3)+2+log2(√35)
=1/4+2+log2(√35)
=9/4+log2(√35)
2、
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]
=(5/6)*(3/2)*lg3/lg2*lg2/lg3
=5/4