If x, y, and z are positive real numbers satisfying:
\(\begin{align*} \log x - \log y &= a, \\ \log y - \log z &= 15, \text{ and} \\ \log z - \log x &= -7, \\ \end{align*}\)
where a is a real number, what is a?
Add all three equations together to get a+8=0 so a is -8
:D
Summing all three equations together, every term on the left-hand side cancels out, yielding that \(0 = a + 15 - 7 \Longrightarrow a = \boxed{-8}\).
+285 
