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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 $a$?

 Jun 20, 2019
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\( log x - log y = a, log y - log z = 15, log z - log x = -7\)

 

log z - log x = -7

log y - log z  = 15        add these and we get

 

logy - log x  =  8       multiply through by -1

 

log x - log y  =  -8 =  "a" 

 

 

cool cool cool

 Jun 20, 2019

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