log2(6)*log3(6)-[log2(3)+log3(2)]的值

问题描述:

log2(6)*log3(6)-[log2(3)+log3(2)]的值

log2(6)*log3(6)-[log2(3)+log3(2)]
=lg6/lg2xlg6/lg3-(lg3/lg2+lg2/lg3)
=(lg6)^2/lg2lg3-[(lg3)^2+(lg2)^2]/lg2lg3
=(lg2+lg3)^2/lg2lg3-[(lg3)^2+(lg2)^2]/lg2lg3
=[(lg2)^2+2lg2lg3+(lg3)^2]/lg2lg3-[(lg3)^2+(lg2)^2]/lg2lg3
=2lg2lg3/lg2lg3
=2