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avatar+289 

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?

 Jan 6, 2021
 #1
avatar+188 
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Add all three equations together to get a+8=0 so a is -8

:D

 Jan 6, 2021
edited by AvenJohn  Jan 6, 2021
 #2
avatar+289 
0

Summing all three equations together, every term on the left-hand side cancels out, yielding that \(0 = a + 15 - 7 \Longrightarrow a = \boxed{-8}\).

 Jan 6, 2021

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