本文研究近几年竞赛中有关指数和对数的赛题,文章从一题多解、一题多变的角度对这些试题进行了探究,以期对考生和一线的老师有所帮助.1.化繁为简,巧妙求值例1(2014年全国联赛一试)若正数a,b满足2+log2a=3+log3b=log6(a+b),则1/a+1/b的值为____.解法1设2+log2a=3+log3b=log6(a+b)=t,那么a=2t-2,b=3t-3,a+b=6t,所以 This paper studies the competitions in recent years index and logarithm of the title, the article from a multi-solution, a change of questions on these questions to explore, with a view to the candidates and teachers help .1. If the positive numbers a and b satisfy 2 + log2a = 3 + log3b = log6 (a + b), then the value of 1 / a + 1 / b is ____. Solution 1 Let 2 + log2a = 3 + log3b = log6 (a + b) = t, then a = 2t-2, b = 3t-3, a + b = 6t,