7. Arrange the three numbers $10 a^{2}+81 a+207, a+2$, and $26-2a$ in such a way that their common logarithms form an arithmetic sequence with a common difference of 1. Then, at this point, $a=$ $\qquad$

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
7. $\frac{1}{2}$.