Question

已知log2(3)=a,log3(7)=b,试用a,b表示log56(42)

Answer 1

已知log2(3)=a,log3(7)=b,
lg3/lg2=a
lg3=alg2
log3(7)=b

lg7/lg3=b
lg7=blg3
lg7=ablg2
log56(42)

=lg(6*7)/lg(7*8)
=(lg6+lg7)/(lg7+lg8)
=(lg2+lg3+lg7)/(lg7+3lg2)
=(lg2+alg2+ablg2)/(ablg2+3lg2)
=(1+a+ab)/(ab+3)

Answer 2

已知log2(3)=a, a=lg3/lg2
log3(7)=b, b=lg7/lg3
log56(42)
=lg42/lg56
=(lg2+lg3+lg7)/(3lg2+lg7)
=(lg2/lg3+1+lg7/lg3)/(3lg2/lg3+lg7/lg3)
=(1/a+1+b)/(3/a+b)
=(1+a+ab)/(3+ab)