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Where the score runs out

Mental mathEasy

In a range game, a range from $L$ to $H$ that contains the true value scores $1 - log_{10} (\frac{H}{L})$ , and a range that misses scores $0$ . A trader's range starts at $L = 40$ and contains the true value. What high end $H$ makes the score exactly $0$ ?

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Hint

Set the score to $0$ and solve for the ratio of the ends first.

Solution

A score of $0$ needs $log_{10} (\frac{H}{L}) = 1$ .
That means the ends differ by a factor of $10$ , so $\frac{H}{L} = 10$ .
Hence $H = 40 \times 10 = 400$ .

Answer: $400$

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