log以2为底9的对数乘于log以3为底4的对数怎么算!
问题描述：
log以2为底9的对数乘于log以3为底4的对数怎么算!
答
原式=lg9/lg2*lg4/lg3=(2lg3/lg2)*(2lg2/lg3)=4
答
log以2为底9的对数乘于log以3为底4的对数
=lg9/lg2xlg4/lg3
=lg9xlg4/(lg2xlg3)
=2lg3x2lg2/(lg2xlg3)
=2x2
=4
答
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