9. Real numbers $a, b, c$ satisfy $5^{a}=2^{b}=\sqrt{10^{c}}$, and $a b \neq 0, \frac{c}{a}+\frac{c}{b}$ has the value of $\qquad$ .
9. 2 .

Let $5^{a}=2^{b}=\sqrt{10^{c}}=k>0$, then $a \lg 5=b \lg 2=\frac{c}{2}=\lg k$, so $\frac{c}{a}+\frac{c}{b}=2 \lg 5+2 \lg 2=2$.