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MATH / If x, y, and z are positive real numbers satisfying: …a is a real number, what is a?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

If xx, yy, and zz 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 aa is a real number, what is aa?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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 $a$?

level

Level 4

type

Algebra

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Source and history

task_id
9c9218b4-0718-53a1-a17d-1ba33f0dadb3
task_key
algebra--test--9c9218b4-0718-53a1-a17d-1ba33f0dadb3
task_revision_id
1
config / split
algebra / test

Official source

initial import