Question

NO.1 (log3 2 + log9 2) (log4 3 + log8 3)

Answer 1

1.原式

=(log3(2)+1/2log3(2))*(2log2(3)+3log2(3))

=3/2*5*log2(3)*log3(2)

=15/2

2.因为（lg5)^2+lg2*lg50

=（lg5)^2+lg2*lg(5*10)

=（lg5)^2+lg2*(lg5+lg10)

=(lg5)^2+lg2(lg5+1)

=lg5*(lg2+lg5)+lg2

=lg5*lg10+lg2

=lg5+lg2=lg(2*5)=lg10=1

3.[(1-log6(3))^2 + log6(2) × log6(18)]÷log6(4)

=[log6(2)^2 + log6(2) × (log6(3)+1)]÷2log6(2)

=(log6(2)+log6(3)+1)/2

=(1+1)/2

=1