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MathNet 2026 — Part 07 Question 122

Math Olympiad Vault · MathNet 2026 — Part 07

Question 122

Consider the system
$$
x y = 10^{a}, \quad y z = 10^{b}, \quad x z = 10^{c}
$$

What is $\log x + \log y + \log z$?
  1. $\frac{a b c}{2}$
  2. $\frac{a+b+c}{2}$
  3. $a+b+c$
  4. $a b c$