Step 1: Write the given equation.
We have $\log_a 2+\log_a 5=1$. Both logarithms share the same base $a$.
Step 2: Combine the two logarithms.
A log rule says $\log_a m+\log_a n=\log_a(mn)$. So adding logs of $2$ and $5$ gives the log of their product.
Step 3: Multiply the numbers.
Since $2\times5=10$, the equation becomes \[ \log_a 10=1. \]
Step 4: Switch to exponential form.
The statement $\log_a 10=1$ means $a$ raised to the power $1$ equals $10$. That is, \[ a^1=10. \]
Step 5: Read off $a$.
Since $a^1=a$, we directly get $a=10$.
Step 6: Quick check.
With $a=10$, $\log_{10}2+\log_{10}5=\log_{10}10=1$, which matches. So the value is correct. \[ \boxed{10} \]