Question

a=log2(3),b=log3(7),用a,b表示log42(56)

Answer 1

解：
c=log42(56)=lg56/lg42=(3lg2+lg7)/(lg2+lg3+lg7)
ab=lg7/lg2, lg7=ablg2.
a=lg3/lg2, lg3=alg2.
代入：c=(3lg2+ablg2)/(lg2+alg2+ablg2)
=(3+ab)/(1+a+ab).

Answer 2

log42(56)=log2(56)/log2(42)=(3+log2(7))/(log2(3)+log2(14))=(3+log3(7)/log3(2))(a+1+log3(7)/log3(2)=(3+ab)/(a+1+ab)