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SMO 2020 Senior Round 1 Question 5

SMO · SMO 2020 Senior Round 1

Question 5

Let $p=\log_{10}(\sin x)$, $q=(\sin x)^{10}$, $r=10^{\sin x}$, where $0\lt x\lt \dfrac\pi2$. Which of the following is true?
  1. $p\lt q\lt r$
  2. $p\lt r\lt q$
  3. $q\lt r\lt p$
  4. $q\lt p\lt r$
  5. $r\lt p\lt q$