若a,b,c是均不为零的实数,且2^6a=3^3b=6^2c从,求证:1/a+2/b=3/c
问题描述：
若a,b,c是均不为零的实数,且2^6a=3^3b=6^2c从,求证:1/a+2/b=3/c
答
证:
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1/a+2/b=3/c
解此题的关键在于设K,然后进行指对互化,再进行对数运算变形即可.