若25^a=4^b=10^c,且abc不等于0,则c/a+c/b=?
问题描述：
若25^a=4^b=10^c,且abc不等于0,则c/a+c/b=?
答
解:
25^a = 4^b = 10^c,
取对数有,
lg(25^a) = lg(4^b) = lg(10^c),
a*lg25 = b*lg4 = c*lg10,
故c/a = lg25/lg10,
c/b = lg4/lg10,
c/a + c/b = lg25/lg10 + lg4/lg10
=(lg25 + lg4) / lg10=lg(25*4) / lg10
=lg(10^2) / lg10=2*lg10 / lg10 = 2,
答案为
c/a + c/b = 2