Rational indicies

2014-01-06 2:34 am
2^a=3^b=6^c (given)

Find the value of (c/a)+ (c/b)
更新1:

Can't use logarithm !!

回答 (1)

2014-01-06 3:13 am
✔ 最佳答案
As 2^a = 6^c2 = (6^c)^(1/a)2 = 6^(c/a) ...... (1)
Similarly 3^b = 6^c3 = (6^c)^(1/b)3 = 6^(c/b) ...... (2)
(1)*(2), get,2*3 = 6^(c/a) * 6^(c/b)==> 6^1 = 6^(c/a + c/b)Therefore,c/a + c/b = 1


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