MathDB
Logarithms

Source:

March 8, 2009
logarithmsprobability

Problem Statement

A non-zero digit is chosen in such a way that the probability of choosing digit d d is \log_{10}(d\plus{}1) \minus{} \log_{10} d. The probability that the digit 2 2 is chosen is exactly 12 \frac12 the probability that the digit chosen is in the set <spanclass=latexbold>(A)</span> {2,3}<spanclass=latexbold>(B)</span> {3,4}<spanclass=latexbold>(C)</span> {4,5,6,7,8}<spanclass=latexbold>(D)</span> {5,6,7,8,9}<spanclass=latexbold>(E)</span> {4,5,6,7,8,9} <span class='latex-bold'>(A)</span>\ \{2,3\} \qquad <span class='latex-bold'>(B)</span>\ \{3,4\} \qquad <span class='latex-bold'>(C)</span>\ \{4,5,6,7,8\} \qquad <span class='latex-bold'>(D)</span>\ \{5,6,7,8,9\} \qquad <span class='latex-bold'>(E)</span>\ \{4,5,6,7,8,9\}