分类：教育/科学-理工学科-数学
问题：对数若log(14)7=a,log(14)5=b,求log(35 
若log()7=a,log(14)5=b,求log(35)28的值
回答：log  7 = lg 7 / lg 14 log 14 5 = lg 5 / lg 14 A = lg 7 / lg 14 = lg 7 / (lg 7 + lg 2) B = lg 5 / lg 14 = (1 - lg2) / (lg 7 + lg 2) 通过以上两式可得: lg 7 = A / (1 - A + B) lg 2 = (1 - A) / (1 - A + B) log 35 28 = lg 28 / lg 35 = (lg 7 + 2lg 2) / (lg 7 + lg 5) = (lg 7 + 2lg 2) / (lg 7 + 1 - lg2) = [A / (1 - A + B) + 2(1 - A) / (1 - A + B)] / [A / (1 - A + B) + 1 - (1 - A) / (1 - A + B)] = [(2 - A) / (1 - A + B)] / [(A + B) / (1 - A + B)] = (2 - A) / (A + B)