log以2为底3的对数是a,log以3为底7的对数是b,求log以42为底56的对数?
问题描述：
log以2为底3的对数是a,log以3为底7的对数是b,求log以42为底56的对数?
答
a=lg3/lg2
lg3=alg2
b=lg7/lg3
lg7=blg3=ablg2
log42(56)
=lg56/lg42
=lg(2^3*7)/lg(2*3*7)
=(3lg2+lg7)/(lg2+lg3+lg7)
=(3lg2+ablg2)/(lg2+alg2+ablg2)
=(3+ab)/(1+a+ab)