若2的6a次方=3的3b次方=6的2c次方,求证1/a+2/b=3/c

设2^6a=3^3b=6^2c=x 所以64^a=27^b=36^c=x
log64 x=a log27 x=b log36 x=c
所以1/a+2/b
=1/log64 x + 2/log27 x
=logx 64 + logx 27^2
=logx 64*27^2=logx 36^3
=3logx 36
=3/log36 x
=3/c