Question

已知3^a=4^b=b^c,且abc≠0，求证：2/a+1/b=2/c

Answer 1

3^a=4^b=6^c
两边取对数
a*lg3=b*lg4=clg6

令a*lg3=b*lg4=clg6=m
1/a=mlg(1/3)
1/b=mlg(1/4)

1/c=mlg(1/6)

2/a+1/b
=2mlg(1/3)+mlg(1/4)
=mlg(1/36)
=2mlg(1/6)
=2/c

Answer 2

设3^a=4^b=6^c=k,
alg3=blg4=clg6=lgk,
2/a+1/b=2lg3/lgk+lg4/lgk=lg36/lgk=2lg6/lgk=2/c.