1题 (lg根号2+lg3-lg根号10)/lg1.82题 已知以6为底7的对数=a,以3为底4的对数是b,求以12为底7的对数?

Question

1题 (lg根号2+lg3-lg根号10)/lg1.8
2题 已知以6为底7的对数=a,以3为底4的对数是b,求以12为底7的对数?

Answer 1

(lg根号2+lg3-lg根号10)/lg1.8
=lg(√2*√9/√10)/lg1.8
=lg√1.8/lg1.8
=(1/2)*lg1.8/lg1.8
=1/2
log6(7)=a
lg7/(lg2+lg3)=a
lg7=alg2+alg3
log3(4)=b
2lg2/lg3=b
lg2=(b/2)lg3
所以lg7=a(b/2)lg3+alg3=(a+ab/2)lg3
log12(7)
=lg7/(2lg2+lg3)
=(a+ab/2)lg3/[2*(b/2)lg3+lg3]
=(a+ab/2)/[2*(b/2)+1]
=(2a+ab)/(2b+2)