OCR C2 — Question 5 8 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeTwo unrelated log parts: both solve equations
DifficultyStandard +0.3 Part (i) requires standard logarithm manipulation (bringing terms to one side, using log laws, solving a quadratic) which is routine C2 content. Part (ii) involves taking logarithms of both sides and rearranging, which is straightforward once the technique is recognized. Both parts are textbook-style exercises with no novel insight required, making this slightly easier than average.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

  1. Solve the equation $$\log_2 (6 - x) = 3 - \log_2 x.$$ [4]
  2. Find the smallest integer \(n\) such that $$3^{n-2} > 8^{250}.$$ [4]

\begin{enumerate}[label=(\roman*)]
\item Solve the equation
$$\log_2 (6 - x) = 3 - \log_2 x.$$ [4]

\item Find the smallest integer $n$ such that
$$3^{n-2} > 8^{250}.$$ [4]
\end{enumerate}

\hfill \mbox{\textit{OCR C2  Q5 [8]}}