Pre-U Pre-U 9794/2 2016 June — Question 2 4 marks

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
Year2016
SessionJune
Marks4
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyEasy -1.2 This is a straightforward exponential equation requiring only basic logarithm manipulation: divide by 4, then apply logarithms to get x = ln(5/4)/ln(3). It's a single-step problem testing routine technique with no conceptual difficulty or problem-solving required, making it easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

Solve the equation \(4 \times 3^x = 5\), giving the solution in an exact form. [4]

AnswerMarks Guidance
\(3^x = \frac{5}{4}\)B1* State \(3^x = \frac{5}{4}\)
\(x = \log_3(\frac{5}{4})\)M1d*, M1d*, A1 [4] Allow using logs before rearranging, as long as valid method to deal with \(\log(4 \times 3^x)\). Take logarithms and apply at least one log rule correctly. Rearrange to make \(x\) the subject. Obtain correct answer aef. Allow BOD if no base specified. ISW decimal answer but not subsequent incorrect log work, such as \(\log(\frac{5}{4})/\log(3) = \log(\frac{5}{12})\).
$3^x = \frac{5}{4}$ | B1* | State $3^x = \frac{5}{4}$

$x = \log_3(\frac{5}{4})$ | M1d*, M1d*, A1 [4] | Allow using logs before rearranging, as long as valid method to deal with $\log(4 \times 3^x)$. Take logarithms and apply at least one log rule correctly. Rearrange to make $x$ the subject. Obtain correct answer aef. Allow BOD if no base specified. ISW decimal answer but not subsequent incorrect log work, such as $\log(\frac{5}{4})/\log(3) = \log(\frac{5}{12})$.
Solve the equation $4 \times 3^x = 5$, giving the solution in an exact form. [4]

\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2016 Q2 [4]}}