已知abc>0且3^a=4^b=6^c求证2/a+1/b=2/c
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log 3^a = log 4^b = log 6^c
a log3 = b log4 = c log6
设
a log3 = b log4 = c log6 = m
2/a = 2log3 /m
1/b = log4 /m
2/c = 2log6 /m
2log3/m + log4/m = 2log3/m + 2log2/m = 2/m * (log3+log2) = 2log6 /m = 2/c
所以 2/a+1/b=2/c
a log3 = b log4 = c log6
设
a log3 = b log4 = c log6 = m
2/a = 2log3 /m
1/b = log4 /m
2/c = 2log6 /m
2log3/m + log4/m = 2log3/m + 2log2/m = 2/m * (log3+log2) = 2log6 /m = 2/c
所以 2/a+1/b=2/c
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