WJEC Unit 1 2023 June — Question 10 11 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2023
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeTwo unrelated log parts: one non-log algebraic part
DifficultyModerate -0.3 Part (a) is a straightforward one-step logarithm equation requiring only exponentiation. Part (b) is a standard exponential equation solved by taking logs. Part (c) requires multiple log law manipulations and is more involved, but follows standard A-level techniques without requiring novel insight. Overall, this is slightly easier than average due to the routine nature of all parts, though part (c) provides some modest challenge through its multi-step algebraic manipulation.
Spec1.06d Natural logarithm: ln(x) function and properties1.06g Equations with exponentials: solve a^x = b

Solve the following equations for values of \(x\).
  1. \(\ln(2x + 5) = 3\) [2]
  2. \(5^{2x+1} = 14\) [3]
  3. \(3\log_7(2x) - \log_7(8x^2) + \log_7 x = \log_3 81\) [6]

Solve the following equations for values of $x$.

\begin{enumerate}[label=(\alph*)]
\item $\ln(2x + 5) = 3$ [2]

\item $5^{2x+1} = 14$ [3]

\item $3\log_7(2x) - \log_7(8x^2) + \log_7 x = \log_3 81$ [6]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 1 2023 Q10 [11]}}