已知a>b>1 且logb/loga+loga/loab=10/3 求logb/loga-loga/loab的值

问题描述:

已知a>b>1 且logb/loga+loga/loab=10/3 求logb/loga-loga/loab的值

logab+logba=10/3 1/logba+logba=10/3
设logba=x 因为a>b>1 所以x>1
1/x+x=10/3 x=1(舍)或3 即使logba=3,logab=1/3
logb/loga-loga/loab=logab-logba=-8/3