Question

5的a次幂=2的b次幂=10的c/2次幂 且abc≠0 则c/a+c/b=

Answer 1

5^a=2^b=10^(c/2)

5^a=10^(c/2)
alg5=c/2lg10
c/a=2lg5/lg10

2^b=10^(c/2)
blg2=c/2lg10
c/b=2lg2/lg10

所以，c/a+c/b=2lg5/lg10+2lg2/lg10
=2(lg5+lg2)/lg10

Answer 2

5^a=2^b=10^(c/2)
a=log(5为底)10^(c/2)
=c/2log(5为底)10
b=log(2为底)10^(c/2)
=c/2log(2为底)10
c/a+c/b
=c/（c/2log(5为底)10）+c/（c/2log(2为底)10）
=2log(5为底)10+2log(2为底)10

Answer 3

2^a=5^b=10^(c/2)
所以a=(c/2)log(2)10 b=(c/2)log(5)10
c/a+c/b
=c/(c/2)log(2)10+c/(c/2)log(5)10
=2log(10)2+2log(10)5
=2log(10)2*5
=2