Question

已知a,b,c均为正数,3^a=4^b=6^c,求证:2/a+1/b=2/c

Answer 1

3^a=4^b=6^c
可令alg3=blg4=clg6=k
a=k/lg3
b=k/lg4
c=k/lg6
2/a+1/b=2lg3/k+lg4/k=2(lg3+lg2)/k=2lg6/k=2/c
证毕

Answer 2

log3^a=log4^b=log6^c
alog3=2blog2=clog6

2/a+1/b=2log3/clog6+2log2/clog6
=2(log2+log3)/clog6
=2log6/clog6
=2/c