+0

# Help

0
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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
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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
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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