Question

若 2^6a=3^3b=6^2c,求证： 3ab-2ac=bc.

Answer 1

设2^6a=3^3b=6^2c=k则6a=log(2,k)=1/log(k,2).

3b=log(3,k）=1/log(k,3)

2c=log(6,k)=1/log(k,6)=1/[log(k,2)+log(k,3)]=1/[1/6a+1/3b]

即1/2c=1/6a+1/3b得3ab-2ac-bc=0

解此题的关键在于设 ,然后进行指对互化,再进行对数运算变形即可.